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arxiv: 2606.05819 · v1 · pith:TJESLG3Unew · submitted 2026-06-04 · 🧮 math.GT

Exotic disks and singular instanton Floer homology

Irving Dai , Abhishek Mallick , Masaki Taniguchi This is my paper

Pith reviewed 2026-06-27 23:06 UTC · model grok-4.3

classification 🧮 math.GT
keywords exotic slice diskssingular instanton Floer homologyZ-slice knotsstrongly invertible knotsChern-Simons filtrationtwo-bridge knotscharacter varietiesequivariant slice disks
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The pith

Singular instanton Floer homology with Chern-Simons filtration distinguishes exotic pairs of slice disks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that the filtered version of singular instanton Floer homology can detect when two slice disks for the same knot are exotic, meaning they are not related by a diffeomorphism of the four-ball fixing the boundary. It produces a concrete example of a strongly invertible Z-slice knot such that every symmetric pair of Z-disks is exotic, and this distinction survives arbitrary stabilizations by CP^2 or its negative. The argument rests on explicit calculations of how the knot's involution acts on the traceless SU(2) character varieties of two-bridge knots, which in turn determine the symmetry actions on the Floer complexes.

Core claim

Singular instanton Floer homology equipped with the Chern-Simons filtration produces exotic pairs of slice disks. For a particular strongly invertible Z-slice knot, every symmetric pair of Z-disks is exotic and remains exotic after stabilization by any number of CP^2 or bar{CP}^2, or by standard RP^2 or its negative. The same methods extend to stabilization by any simply connected definite four-manifold or by exotic projective planes of fixed sign. Along the way the symmetry actions on the singular instanton complexes of two-bridge knots are computed via their traceless SU(2) character varieties.

What carries the argument

singular instanton Floer homology with the Chern-Simons filtration, carrying symmetry actions induced by the knot involution and computed from traceless SU(2) character varieties

If this is right

  • There exist Z-slice knots that are strongly invertible yet admit no equivariantly standard symmetric Z-disks.
  • Exoticness of the disks persists under stabilization by any simply connected definite four-manifold.
  • The same filtered homology distinguishes exotic symmetric pairs after stabilization by any number of exotic projective planes of one sign.
  • There are knots that are both Z-slice and equivariantly slice but not equivariantly Z-slice.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same character-variety techniques could be applied to other families of knots whose traceless SU(2) representations are explicitly describable.
  • If the filtered homology is functorial under cobordisms that respect the involution, it would give obstructions in the equivariant setting beyond what unfiltered theories supply.
  • The construction suggests that exotic disks may be detected by other filtered instanton-type invariants once their symmetry actions are computed.

Load-bearing premise

The explicit analysis of traceless SU(2) character varieties of two-bridge knots correctly identifies the symmetry actions on the singular instanton Floer complexes.

What would settle it

An explicit pair of symmetric Z-disks for the constructed knot whose induced filtered complexes are isomorphic would show that the homology does not distinguish them.

Figures

Figures reproduced from arXiv: 2606.05819 by Abhishek Mallick, Irving Dai, Masaki Taniguchi.

Figure 1
Figure 1. Figure 1: The concordance C from K to K1 , together with the concordance Γ from Fixpτ q to Fixpτ 1 q. We draw C as a cylinder and draw (part of) Γ as the vertical sheet. In this picture, C XΓ consists of a pair of arcs that divides Γ into two rectangles. The component containing the half-axes for K and K1 is visible as the central rectangle. It is straightforward to check that isotopy-equivariant concordance is comp… view at source ↗
Figure 2
Figure 2. Figure 2: The flip map τf on T2,3#T r 2,3 . Suppose moreover that J itself is strongly invertible with some strong inversion τ0. We may then consider the strongly invertible knot p2J# ´ 2J, τf# ´ 2τ0q, as displayed in [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Left: the unique strong inversion p´qτ0 on the trefoil p´qT2,3. Right: the slice knot K “ 2T2,3# ´ 2T2,3, equipped with the strong inversion τ “ τf# ´ 2τ0. Example 2.22. Let pK, τ q be a strongly invertible knot in S 3 . Then we may form the (multiply￾clasped) Whitehead double WhipKq of K, as in [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The i-clasped Whitehead double WhipKq for i “ 2. Left: the original strongly invertible knot K, with fixed points drawn at the top and bottom of K. The arrow represents a choice of direction. Middle: placing the clasp at the foot of the indicated direction. Right: placing the clasp at the head of the indicated direction. Now take the branched double cover Σ2pWhipKqq. We wish to identify the involution on Σ… view at source ↗
Figure 5
Figure 5. Figure 5: Left: a Whitehead double with the clasp drawn inside a small green 3-ball. Middle: replacing the clasp with a trivial tangle so that the result is an unknot. Right: isotoping the green 3-ball along K so that the black knot becomes a local unknot. K K K K [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Left: the result of placing the clasp at the foot of the direction. Right: the result of placing the clasp at the head of the direction. The reader may refer to [DHMS24] for further discussion and to verify that the surgery coefficient is indeed 1{p2iq. Note, however, that the formation of K#Kr depends on which fixed point is used to form the clasp. Indeed, in [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Illustration of strong inversions on K#Kr in the case K “ 2T2,3#´2T2,3, equipped with the involution τ “ τf#´2τ0. The involution τ#τ r is given by rotation about the horizontal axis; this corresponds to one of the lifts of τ on WhipKq to Σ2pWhipKqq. The involution corresponding to the branching action q is given by rotation about the vertical axis. 3. Singular instanton theory In this section, we give a ra… view at source ↗
Figure 8
Figure 8. Figure 8: Paths on pW, Sq and pW: , S: q. With this in hand, we now define Daemi and Scaduto’s connected sum map λr :“ λr pW,Sq : CrpY, K, x0q b CrpY 1 , K1 , x1 0 q Ñ CrpY #Y 1 , K#K1 , x#q [PITH_FULL_IMAGE:figures/full_fig_p040_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: In [DS24b, Section 6], it is shown that rr [PITH_FULL_IMAGE:figures/full_fig_p041_10.png] view at source ↗
Figure 9
Figure 9. Figure 9: Construction of λr. We cut down our moduli spaces by the holonomy conditions associated to the green curves. A red dot represents a reducible limit at the indicated end. The rows construct λ, µ, ∆1, and ∆2, respectively. e ¤ . . e e e [PITH_FULL_IMAGE:figures/full_fig_p042_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Construction of λr. We cut down our moduli spaces by the holonomy conditions associated to the green curves. A red dot represents a reducible limit at the indicated end. The rows construct λ 1 , µ 1 , ∆1 1 , and ∆1 2 , respectively. PPP ↑ [PITH_FULL_IMAGE:figures/full_fig_p042_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: 二 Extensions of τ \ τ 1 and τ#τ 1 [PITH_FULL_IMAGE:figures/full_fig_p042_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Boundary degenerations leading to (23) through (26). Each of these comes from analyzing the boundaries of the compactified 1-dimensional moduli spaces M` γ pα, β; θq, M`pα, β; θq, M`pα, θ; θq, and M`pθ, β; θq, respectively. We show the topological degenerations leading to (27) through (30) in [PITH_FULL_IMAGE:figures/full_fig_p046_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Boundary degenerations leading to (27) through (30). We now prove that the map λr1 in the other direction is weakly involutive. This means we claim there is an S-homotopy Gr : CrpY #Y 1 , K#K1 , x#q Ñ CrpY, K, x0q b CrpY 1 , K1 , x1 0 q such that drbGr ` Grdr# “ λr1 ˝ τr 7 ` τr b ˝ λr1 ` E21. As usual, it suffices to give the components of the homotopy Gr “ » – G 0 0 µ G G ∆G 2 ∆G 1 0 0 fi fl , where ‚ G … view at source ↗
Figure 14
Figure 14. Figure 14 [PITH_FULL_IMAGE:figures/full_fig_p049_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Left: the complex CpT2,3q ‘ R. Right: the complex CpT2,3 b T2,3q ‘ R. In an unfortunate collision of notation, the generator 0 denotes the reducible and 1 denotes the irreducible, while in our usual notation for C b, the reducible of each factor is denoted 1. We make this change for consistency with more general calculations in later sections. All arrows have a coefficient of Λ. Gradings are arranged by h… view at source ↗
Figure 16
Figure 16. Figure 16: Left: the action of τ0#τ0. Right: the action of τf . The only nontrivial τ -component is represented by the horizontal dotted arrow. The µ τ -components are given by the red dashed arrows. The vertical red dashed arrow has a coefficient of 1; the other dashed arrows have coefficients of c1 and c2, respectively. In the case of τf , we have Λ|pc1 ` c2q. 6. The Chern–Simons filtration In this section, we int… view at source ↗
Figure 17
Figure 17. Figure 17: Equivariant cobordism from 1{n-surgery to 1{pn ´ 1q. The symmetry is with respect to the horizontal axis. It is straightforward to equip this with an invariant annulus Sn running from a local unknot U Ă Yn to a local unknot U Ă Yn´1 and check that this is a strong negative definite pair. Clearly, π1pWn z Snq “ Z. Hence by Theorem 6.1(2), ¨ ¨ ¨ ă r0pY3, U, τ q ă r0pY2, U, τ q ă r0pY1, U, τ q ă 8. Moreover,… view at source ↗
Figure 18
Figure 18. Figure 18 [PITH_FULL_IMAGE:figures/full_fig_p067_18.png] view at source ↗
Figure 18
Figure 18. Figure 18: Left: the complex for p2T2,3, τf q and the complex for p´2T2,3, ´2τ0q. Right: the complex for p2T2,3, 2τ0q and the complex for p´2T2,3, ´τf q. We now investigate the rs-invariant. Since the rs-invariant can be defined in terms of the under-bar complex, we do not have to calculate the µ b-component of the tensor product. (Indeed, our partial connected sum formula does not allow us to calculate this compone… view at source ↗
Figure 19
Figure 19. Figure 19: Construction of an equivariant negative definite cobordism from S 3 1 p946#946q to S 3 1 p946q. The symmetry is with respect to rotation along the ver￾tical line, in the second step we have applied an equivariant isotopy. □ [PITH_FULL_IMAGE:figures/full_fig_p071_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: The unique strong inversion τ0 on the torus knot T2,2n`1. The arc γ is given by the red segment (passing over the point at 8). There are 2n ` 1-many half crossings. We claim that the lift (or, more precisely, both lifts) of τ0 act as the identity on the representation variety. Indeed, consider a neighborhood of the arc γ indicated in [PITH_FULL_IMAGE:figures/full_fig_p073_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: (See [Sak86, Figure 3.2].) As we will see, these two inversions behave quite similarly for [PITH_FULL_IMAGE:figures/full_fig_p073_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: The two strong inversion τ0 and τ1 on Kp,q when q 2 ‰ 1 mod p. The arc γ is given by the red segment. The β-circle is shown in green. Here q{p “ r2, 4, ´4, ´2s. As before, τ0 acts as the identity on the representation variety since it preserves Npγq. However, note that τ1 does not preserve Npγq. Instead, to understand the action of τ1 on π1pLpp, qqq, consider the diagram for Kp,q given in [PITH_FULL_IMAG… view at source ↗
Figure 23
Figure 23. Figure 23: The involution τ1 drawn in a different diagram. We now use our understanding of these actions on the representation variety to perform a partial computation of τ on the instanton knot complex. It will first be useful to verify that the lift of each symmetry of Kp,q is covered by an involution on S 3 which preserves the standard round metric: Lemma 8.1. Let τ be an involution on Lpp, qq obtained by lifting… view at source ↗
Figure 24
Figure 24. Figure 24: The results of [DS24b, Section 9] and Theorem 8.2 for K “ K15,4. Gen￾erators are enumerated from 0 to pp ´ 1q{2 “ 7 with a subscript of n representing Chern-Simons degree n{15. Solid arrows represent the differential and the δ1- and δ2-maps. Red dashed lines are possible v-maps; the actual v-map is some subset of the red arrows. Dotted horizontal arrows represent the action of τ1; if no dotted arrow is dr… view at source ↗
Figure 25
Figure 25. Figure 25: The results of [DS24b, Section 9] and Theorem 8.2 for K45,26. Conven￾tions are similar to [PITH_FULL_IMAGE:figures/full_fig_p079_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Examples of standard complexes. The action of U is given by vertical translation. Dashed arrows depict the action of ω “ 1 ` ι; solid arrows denote the differential. Note that the first two complexes are genuine ι-complexes. The third is only an almost ι-complex, since pB ˝ ωq and pω ˝ Bq are only equal modulo U on (for example) x2. In [DHST23, Section 6], it is shown that every almost ι-complex is locall… view at source ↗
Figure 27
Figure 27. Figure 27: Left: the complex pCFKpT2,3, ιKτ0q. Middle: the complex A “ 2pCFKpT2,3, ιKτ0q. Right: the complex B “ pCFKp2T2,3, ιKτf q. We have drawn the action of 1 ` ιKτK using the dotted arrows. If no dotted arrow is drawn, the action of 1 ` ιKτK is zero. The following are not difficult to see: (1) We have B ď A. Indeed, a local map from B to A is provided by mapping the staircase isomorphically onto the staircase, … view at source ↗
Figure 28
Figure 28. Figure 28: The standard complex S in the proof of Lemma 9.11 [PITH_FULL_IMAGE:figures/full_fig_p088_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: The standard complex S in the proof of Lemma 9.12. Note the direction of the arrow from x2k´1 to x2k. Now, x2k does not appear in the image of B except with a power of U, so there is no term from UBq which can cancel with Ux2k. In particular, the left-hand expression is in the image of U 2 , while the right-hand expression is not. Hence it is impossible to find a lift of ω mod U such that ω ˝ B “ B ˝ ω. T… view at source ↗
read the original abstract

We show that singular instanton Floer homology with the Chern--Simons filtration can be used to produce exotic pairs of slice disks. We moreover construct a strongly invertible $\mathbb{Z}$-slice knot for which any symmetric pair of $\mathbb{Z}$-disks are exotic, and remain exotic after stabilizing by $n\smash{\mathbb{CP}}^2$ or $n\smash{\overline{\mathbb{CP}}}^2$ (or by standard $n\smash{\mathbb{RP}}^2$ or $-n\smash{\mathbb{RP}}^2$) for any $n$. Our methods apply more generally to stabilization by any simply connected definite manifold, or by any number of exotic embedded projective planes of the same sign. We also provide an example of a strongly invertible knot which is $\mathbb{Z}$-slice and equivariantly slice, but not equivariantly $\mathbb{Z}$-slice. Along the way, we partially compute various symmetry actions on the singular instanton Floer complexes of two-bridge knots via an explicit analysis of their traceless $\mathit{SU}(2)$-character varieties.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript shows that singular instanton Floer homology equipped with the Chern-Simons filtration can be used to produce exotic pairs of slice disks. It constructs a strongly invertible Z-slice knot for which every symmetric pair of Z-disks is exotic, with this exoticity persisting after stabilization by n CP^2 or n bar{CP}^2 (or by standard n RP^2 or -n RP^2) for any n, and more generally after stabilization by any simply connected definite 4-manifold or by any number of exotic embedded projective planes of the same sign. It also exhibits a strongly invertible knot that is Z-slice and equivariantly slice but not equivariantly Z-slice. The arguments rely on explicit partial computations of symmetry actions on the singular instanton Floer complexes of two-bridge knots, obtained via analysis of their traceless SU(2)-character varieties.

Significance. If the central computations are correct, the work supplies a new Floer-theoretic method for distinguishing exotic slice disks, including in the equivariant and stabilized settings. The construction of a knot that is Z-slice and equivariantly slice yet fails to be equivariantly Z-slice, together with the persistence of exoticity under arbitrary stabilizations by definite manifolds, strengthens the toolkit for detecting exotic phenomena in 4-manifolds. The explicit character-variety computations of symmetry actions constitute a concrete, verifiable contribution that can be checked independently.

minor comments (3)
  1. The statement of the main theorem on stabilization (likely Theorem 1.1 or 1.2) would be clearer if the cases for simply connected definite manifolds and exotic projective planes were enumerated separately rather than grouped under a single sentence.
  2. In the section describing the character variety computations for two-bridge knots, a short table or diagram summarizing the fixed-point sets under the involutions would help the reader track the symmetry actions on the generators of the Floer complex.
  3. A few instances of inconsistent capitalization appear in the notation for the Chern-Simons filtration (e.g., "Chern-Simons" versus "Chern--Simons"); these should be standardized.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive and detailed summary of our manuscript, as well as for the favorable assessment of its significance. We appreciate the recommendation of minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper derives its results on exotic slice disks from explicit computations of traceless SU(2)-character varieties of two-bridge knots, which determine symmetry actions on the singular instanton Floer complexes with Chern-Simons filtration. These computations are presented as independent mathematical analysis rather than any self-definitional equivalence, fitted parameter renamed as prediction, or load-bearing self-citation chain. No step in the provided abstract or claim description reduces the central claim to its own inputs by construction; the argument remains self-contained against external benchmarks such as direct character variety calculations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on the established framework of singular instanton Floer homology and properties of SU(2) character varieties for two-bridge knots; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • standard math Standard background results in instanton Floer homology and 4-manifold topology hold.
    The claims depend on the well-definedness and functoriality of the singular instanton Floer complexes with Chern-Simons filtration.

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Works this paper leans on

299 extracted references · 50 canonical work pages

  1. [1]

    Geometry & Topology , volume =

    Conway, Anthony and Powell, Mark , title =. Geometry & Topology , volume =. 2023 , pages =

    2023

  2. [2]

    Comptes Rendus de l'Acad

    Perron, Bernard , title =. Comptes Rendus de l'Acad. 1984 , pages =

    1984

  3. [3]

    Topology , volume =

    Perron, Bernard , title =. Topology , volume =. 1986 , pages =

    1986

  4. [4]

    Journal of Differential Geometry , volume =

    Quinn, Frank , title =. Journal of Differential Geometry , volume =. 1986 , pages =

    1986

  5. [5]

    Algebraic & Geometric Topology , volume=

    Characterizing slopes for torus knots , author=. Algebraic & Geometric Topology , volume=. 2014 , publisher=

    2014

  6. [6]

    Inanc and Sunukjian, Nathan , title =

    Baykur, R. Inanc and Sunukjian, Nathan , title =. Journal of Topology , volume =. 2016 , doi =. 1504.04086 , archivePrefix =

    Pith/arXiv arXiv 2016

  7. [7]

    Advances in Mathematics , volume =

    Auckly, Dave and Kim, Hee Jung and Melvin, Paul and Ruberman, Daniel and Schwartz, Hannah , title =. Advances in Mathematics , volume =. 2019 , doi =. 1708.03208 , archivePrefix =

    Pith/arXiv arXiv 2019

  8. [8]

    Transactions of the American Mathematical Society , volume =

    Kim, Hee Jung , title =. Transactions of the American Mathematical Society , volume =. 2019 , doi =. 1701.02337 , archivePrefix =

    Pith/arXiv arXiv 2019

  9. [9]

    Transverse invariants and exotic surfaces in the 4-ball , JOURNAL =

    Juh\'. Transverse invariants and exotic surfaces in the 4-ball , JOURNAL =. 2021 , NUMBER =. doi:10.2140/gt.2021.25.2963 , URL =

    work page doi:10.2140/gt.2021.25.2963 2021

  10. [10]

    2026 , eprint=

    Basepoints in Khovanov homology and nonorientable surfaces , author=. 2026 , eprint=

    2026

  11. [11]

    Sarkar, Sucharit , TITLE =. Algebr. Geom. Topol. , FJOURNAL =. 2015 , NUMBER =. doi:10.2140/agt.2015.15.2479 , URL =

    work page doi:10.2140/agt.2015.15.2479 2015

  12. [12]

    Zemke, Ian , TITLE =. Algebr. Geom. Topol. , FJOURNAL =. 2017 , NUMBER =. doi:10.2140/agt.2017.17.3461 , URL =

    work page doi:10.2140/agt.2017.17.3461 2017

  13. [13]

    Hayden, Kyle and Sundberg, Isaac , TITLE =. J. Reine Angew. Math. , FJOURNAL =. 2024 , PAGES =. doi:10.1515/crelle-2024-0001 , URL =

    work page doi:10.1515/crelle-2024-0001 2024

  14. [14]

    2023 , eprint =

    Hayden, Kyle and Kang, Sungkyung and Mukherjee, Anubhav , title =. 2023 , eprint =

    2023

  15. [15]

    Rank-expanding satellites,

    Dai, Irving and Hedden, Matthew and Mallick, Abhishek and Stoffregen, Matthew , journal=. Rank-expanding satellites,. 2024 , publisher=

    2024

  16. [16]

    Proceedings of the American Mathematical Society , volume =

    Satoh, Shin , title =. Proceedings of the American Mathematical Society , volume =. 2005 , doi =

    2005

  17. [17]

    Osaka Journal of Mathematics , volume =

    Kamada, Seiichi , title =. Osaka Journal of Mathematics , volume =. 1989 , doi =

    1989

  18. [18]

    Transactions of the American Mathematical Society , volume =

    Boyle, Jeffrey , title =. Transactions of the American Mathematical Society , volume =. 1988 , doi =

    1988

  19. [19]

    Journal of Knot Theory and Its Ramifications , volume =

    Satoh, Shin , title =. Journal of Knot Theory and Its Ramifications , volume =. 2002 , doi =

    2002

  20. [20]

    Atiyah, M. F. and Drinfeld, V. G. and Hitchin, N. J. and Manin, Yu. I. , title =. Physics Letters A , volume =. 1978 , doi =

    1978

  21. [21]

    Boletin de la Sociedad Matematica Mexicana , series =

    Kamada, Seiichi , title =. Boletin de la Sociedad Matematica Mexicana , series =. 2014 , doi =. 1403.0690 , archivePrefix =

    Pith/arXiv arXiv 2014

  22. [22]

    Geometriae Dedicata , volume =

    Longo, Vincent , title =. Geometriae Dedicata , volume =. 2020 , doi =. 1901.10972 , archivePrefix =

    Pith/arXiv arXiv 2020

  23. [23]

    Journal of Topology , volume =

    Auckly, David and Sadykov, Rustam , title =. Journal of Topology , volume =. 2021 , doi =. 1808.08605 , archivePrefix =

    arXiv 2021

  24. [24]

    Journal of the European Mathematical Society , year =

    Conway, Anthony and Orson, Patrick and Powell, Mark , title =. Journal of the European Mathematical Society , year =. doi:10.4171/JEMS/1638 , eprint =

    work page doi:10.4171/jems/1638

  25. [25]

    2023 , eprint =

    Miyazawa, Jin , title =. 2023 , eprint =

    2023

  26. [26]

    International Mathematics Research Notices , volume =

    Dai, Irving and Mallick, Abhishek and Zemke, Ian , title =. International Mathematics Research Notices , volume =. 2024 , eprint =

    2024

  27. [27]

    Selecta Mathematica

    Konno, Hokuto and Mallick, Abhishek and Taniguchi, Masaki , title =. Selecta Mathematica. New Series , volume =. 2026 , eprint =

    2026

  28. [28]

    2022 , eprint =

    Kang, Sungkyung , title =. 2022 , eprint =

    2022

  29. [29]

    arXiv preprint arXiv:2409.16390 , year=

    Unoriented skein exact triangles in equivariant singular instanton Floer theory , author=. arXiv preprint arXiv:2409.16390 , year=

    arXiv

  30. [30]

    Instanton

    Collin, Olivier and Steer, Brian , journal=. Instanton. 1999 , publisher=

    1999

  31. [31]

    Topology , volume=

    Floer homology of connected sum of homology 3-spheres , author=. Topology , volume=. 1996 , publisher=

    1996

  32. [32]

    2024 , Eprint =

    Taketo Sano , Title =. 2024 , Eprint =

    2024

  33. [33]

    2024 , Eprint =

    Keegan Boyle and Wenzhao Chen , Title =. 2024 , Eprint =

    2024

  34. [34]

    Hodgson, Craig and Rubinstein, J. H. , TITLE =. Knot theory and manifolds (. 1985 , MRCLASS =. doi:10.1007/BFb0075012 , URL =

    work page doi:10.1007/bfb0075012 1985

  35. [35]

    2023 , eprint=

    Doubled Disks and Satellite Surfaces , author=. 2023 , eprint=

    2023

  36. [36]

    Journal of Topology , volume=

    Knot homology groups from instantons , author=. Journal of Topology , volume=. 2011 , publisher=

    2011

  37. [37]

    Topology , volume=

    An obstruction to removing intersection points in immersed surfaces , author=. Topology , volume=. 1997 , publisher=

    1997

  38. [38]

    Algebraic and topological theories (

    Sakuma, Makoto , TITLE =. Algebraic and topological theories (. 1986 , MRCLASS =

    1986

  39. [39]

    Mathematical Surveys and Monographs , volume=

    K3: A New Problem List in Low-Dimensional Topology , author =. Mathematical Surveys and Monographs , volume=

  40. [40]

    Involutions and the

    Antonio Alfieri and Irving Dai and Abhishek Mallick and Masaki Taniguchi , year=. Involutions and the. 2309.02309 , archivePrefix=

    arXiv

  41. [41]

    , TITLE =

    Hirsch, Morris W. , TITLE =. 1994 , PAGES =

    1994

  42. [42]

    Michigan Math

    Alfieri, Antonio and Boyle, Keegan , TITLE =. Michigan Math. J. , FJOURNAL =. 2024 , NUMBER =. doi:10.1307/mmj/20226183 , URL =

    work page doi:10.1307/mmj/20226183 2024

  43. [43]

    Topology , FJOURNAL =

    Waldhausen, Friedhelm , TITLE =. Topology , FJOURNAL =. 1969 , PAGES =. doi:10.1016/0040-9383(69)90033-0 , URL =

    work page doi:10.1016/0040-9383(69)90033-0 1969

  44. [44]

    Pacific J

    Myers, Robert , TITLE =. Pacific J. Math. , FJOURNAL =. 1981 , NUMBER =

    1981

  45. [45]

    Boyle, Keegan and Issa, Ahmad , TITLE =. J. Topol. , FJOURNAL =. 2022 , NUMBER =. doi:10.1112/topo.12254 , URL =

    work page doi:10.1112/topo.12254 2022

  46. [46]

    Tautological classes of definite 4-manifolds , url =

    Baraglia, David , date-added =. Tautological classes of definite 4-manifolds , url =. Geom. Topol. , mrclass =. 2023 , bdsk-url-1 =. doi:10.2140/gt.2023.27.641 , fjournal =

    work page doi:10.2140/gt.2023.27.641 2023

  47. [47]

    Sato, Kouki , date-added =. The. Selecta Math. (N.S.) , mrclass =. 2023 , bdsk-url-1 =. doi:10.1007/s00029-023-00867-6 , fjournal =

    work page doi:10.1007/s00029-023-00867-6 2023

  48. [48]

    Corks, involutions, and

    Dai, Irving and Hedden, Matthew and Mallick, Abhishek , date-added =. Corks, involutions, and. J. Eur. Math. Soc. (JEMS) , mrclass =. 2023 , bdsk-url-1 =. doi:10.4171/jems/1239 , fjournal =

    work page doi:10.4171/jems/1239 2023

  49. [49]

    Filtered instanton

    Yuta Nozaki and Kouki Sato and Masaki Taniguchi , date-added =. Filtered instanton. 2023 , bdsk-url-1 =. doi:10.4171/JEMS/1371 , journal =

    work page doi:10.4171/jems/1371 2023

  50. [50]

    arXiv preprint arXiv:2005.08928 , title =

    Kyle Hayden and Lisa Piccirillo , date-added =. arXiv preprint arXiv:2005.08928 , title =

    arXiv 2005

  51. [51]

    On homology cobordism and local equivalence between plumbed manifolds , url =

    Dai, Irving and Stoffregen, Matthew , date-added =. On homology cobordism and local equivalence between plumbed manifolds , url =. Geom. Topol. , mrclass =. 2019 , bdsk-url-1 =. doi:10.2140/gt.2019.23.865 , fjournal =

    work page doi:10.2140/gt.2019.23.865 2019

  52. [52]

    Existence of

    Nagami, Seiji , date-added =. Existence of. Osaka J. Math. , mrclass =. 2000 , bdsk-url-1 =

    2000

  53. [53]

    Correction terms and the nonorientable slice genus , url =

    Golla, Marco and Marengon, Marco , date-added =. Correction terms and the nonorientable slice genus , url =. Michigan Math. J. , mrclass =. 2018 , bdsk-url-1 =. doi:10.1307/mmj/1511924604 , fjournal =

    work page doi:10.1307/mmj/1511924604 2018

  54. [54]

    and Livingston, Charles , date-added =

    Gilmer, Patrick M. and Livingston, Charles , date-added =. The nonorientable 4-genus of knots , url =. J. Lond. Math. Soc. (2) , mrclass =. 2011 , bdsk-url-1 =. doi:10.1112/jlms/jdr024 , fjournal =

    work page doi:10.1112/jlms/jdr024 2011

  55. [55]

    arXiv preprint arXiv:2007.14332 , title =

    Samantha Allen , date-added =. arXiv preprint arXiv:2007.14332 , title =

    arXiv 2007

  56. [56]

    arXiv preprint arXiv:2307.08130 , title =

    Adam Simon Levine and Tye Lidman and Lisa Piccirillo , date-added =. arXiv preprint arXiv:2307.08130 , title =

    arXiv

  57. [57]

    Scaduto, Christopher W. , doi =. Instantons and odd. J. Topol. , mrclass =. 2015 , bdsk-url-1 =

    2015

  58. [58]

    Kronheimer, P. B. and Mrowka, T. S. , doi =. Khovanov homology is an unknot-detector , url =. Publ. Math. Inst. Hautes \'. 2011 , bdsk-url-1 =

    2011

  59. [59]

    Handle decomposition complexibility and representation spaces , year =

    Paolo Aceto and Aliakbar Daemi and Jennifer Hom and Tye Lidman and JungHwan Park , eprint =. Handle decomposition complexibility and representation spaces , year =

  60. [60]

    Duke Math

    Daemi, Aliakbar , TITLE =. Duke Math. J. , FJOURNAL =. 2020 , NUMBER =. doi:10.1215/00127094-2020-0017 , URL =

    work page doi:10.1215/00127094-2020-0017 2020

  61. [61]

    Nonorientable slice genus can be arbitrarily large , url =

    Batson, Joshua , date-added =. Nonorientable slice genus can be arbitrarily large , url =. Math. Res. Lett. , mrclass =. 2014 , bdsk-url-1 =. doi:10.4310/MRL.2014.v21.n3.a1 , fjournal =

    work page doi:10.4310/mrl.2014.v21.n3.a1 2014

  62. [62]

    arXiv:2306.12305 , title =

    Conway, Anthony and Orson, Patrick and Powell, Mark , date-added =. arXiv:2306.12305 , title =

    arXiv

  63. [63]

    Massey, W. S. , date-added =. Proof of a conjecture of. Pacific J. Math. , mrclass =. 1969 , bdsk-url-1 =

    1969

  64. [64]

    Unoriented knot

    Ozsv\'. Unoriented knot. Int. Math. Res. Not. IMRN , mrclass =. 2017 , bdsk-url-1 =. doi:10.1093/imrn/rnw143 , fjournal =

    work page doi:10.1093/imrn/rnw143 2017

  65. [65]

    Gordon, C. McA. and Litherland, R. A. , date-added =. On the signature of a link , url =. Invent. Math. , mrclass =. 1978 , bdsk-url-1 =. doi:10.1007/BF01609479 , fjournal =

    work page doi:10.1007/bf01609479 1978

  66. [66]

    Stable isotopy in four dimensions , url =

    Auckly, Dave and Kim, Hee Jung and Melvin, Paul and Ruberman, Daniel , date-added =. Stable isotopy in four dimensions , url =. J. Lond. Math. Soc. (2) , mrclass =. 2015 , bdsk-url-1 =. doi:10.1112/jlms/jdu075 , fjournal =

    work page doi:10.1112/jlms/jdu075 2015

  67. [67]

    Floer homology for 2-torsion instanton invariants , url =

    Sasahira, Hirofumi , doi =. Floer homology for 2-torsion instanton invariants , url =. Asian J. Math. , mrclass =. 2013 , bdsk-url-1 =

    2013

  68. [68]

    On negative-definite cobordisms among lens spaces of type

    Fukumoto, Yoshihiro , doi =. On negative-definite cobordisms among lens spaces of type. Algebr. Geom. Topol. , mrclass =. 2019 , bdsk-url-1 =

    2019

  69. [69]

    arXiv preprint arXiv:2011.00113 , title =

    Hendricks, Kristen and Hom, Jennifer and Stoffregen, Matthew and Zemke, Ian , date-added =. arXiv preprint arXiv:2011.00113 , title =

    arXiv 2011

  70. [71]

    Instantons and rational homology spheres , year =

    Daemi, Aliakbar and Eismeier, Mike Miller , journal =. Instantons and rational homology spheres , year =

  71. [72]

    arXiv preprint arXiv:2209.05400 , year=

    Instantons, special cycles, and knot concordance , author=. arXiv preprint arXiv:2209.05400 , year=

    arXiv

  72. [73]

    New York J

    Ruberman, Daniel , TITLE =. New York J. Math. , FJOURNAL =. 2016 , PAGES =

    2016

  73. [74]

    Equivariant

    Miller, Stephen Michael , isbn =. Equivariant. 2019 , bdsk-url-1 =

    2019

  74. [75]

    2025 , Eprint =

    Hayato Imori and Taketo Sano and Kouki Sato and Masaki Taniguchi , Title =. 2025 , Eprint =

    2025

  75. [76]

    Quantum Topology , volume=

    Filtrations on instanton homology , author=. Quantum Topology , volume=

  76. [77]

    2025 , Eprint =

    Maciej Borodzik and Irving Dai and Abhishek Mallick and Matthew Stoffregen , Title =. 2025 , Eprint =

    2025

  77. [78]

    Equivariant

    Austin, David M and Braam, Peter J , journal=. Equivariant. 1996 , publisher=

    1996

  78. [79]

    Advances in Mathematics , volume=

    2-torsion in instanton Floer homology , author=. Advances in Mathematics , volume=. 2025 , publisher=

    2025

  79. [80]

    Framed instanton homology and Fr

    Ghosh, Sudipta and Miller Eismeier, Mike , journal=. Framed instanton homology and Fr

  80. [81]

    arXiv preprint arXiv:2307.03950 , year=

    Mod 2 instanton homology and 4-manifolds with boundary , author=. arXiv preprint arXiv:2307.03950 , year=

    arXiv

Showing first 80 references.