$ L_\infty $-spectral sequences for Hochschild cohomology

Jasper van de Kreeke

REVIEW 3 major objections 6 minor 18 references

$ L_\infty $-spectral sequences for Hochschild cohomology

T0 review · 3 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Twisting a simpler complex by a Maurer-Cartan element lets a spectral sequence keep the higher L∞-structure on cohomology; for gentle algebras the Hochschild complex is explicitly L∞-quasi-isomorphic to its cohomology.

desk verdict A promising new L∞-transfer framework whose main application rests on an unproved identification in Lemma 4.7 – likely fixable, but not yet a complete proof. read the letter →

arxiv 2508.21716 v1 pith:JOLGJBXX submitted 2025-08-29 math.AT math.KTmath.RT

Jasper van de Kreeke This is my paper · ORCID

classification math.ATmath.KTmath.RT MSC 16E4018G4053D37

keywords L∞-algebrasspectralsequencesMaurer-CartantwistingHochschildcohomologygentlealgebrasA∞-categoriesminimalmodelsformality

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Spectral sequences compute cohomology vector spaces but usually discard the higher multiplicative structure (A∞-, L∞-) carried by the original complex. This paper argues that when the complex with higher structure is a twisting of a simpler complex by a Maurer-Cartan element — as the Hochschild complex of a minimal A∞-category is obtained from the associative Hochschild complex by twisting with the higher products μ≥3 — one can set up a 'spectral sequence' whose differentials are the twisted differentials and whose pages are transferred L∞-minimal models. The central claim is that, for punctured-surface gentle algebras, the resulting spectral inclusion is an L∞-quasi-isomorphism: the Hochschild complex of the A∞-gentle algebra is L∞-quasi-isomorphic to its cohomology, recovering formality and giving the higher structure explicitly. The result replaces the earlier fragile grading argument for formality with a structural one, and it supplies a recipe for other twisted DGLAs.

What carries the argument

The central objects are (1) the spectral DGLA LW = (V, d0+[W,−],[−,−]), a DGLA twisted by an almost-pronilpotent Maurer-Cartan element W (a degree-one element solving dW+½[W,W]=0), and (2) the two-step spectral inclusion iWH ∘ i′ : H((HL)WH) → (HL)WH → LW. Here HL is the minimal model of the untwisted DGLA L, WH is a Maurer-Cartan element of HL whose image under the minimal-model inclusion equals W, and iWH is the inclusion twisted around WH. The computation is carried by Kadeishvili-tree formulas from homological perturbation, which give the L∞-brackets and the inclusion explicitly, and by a homological splitting of the gentle-algebra Hochschild complex that computes the brackets and verifi

What would settle it

Explicitly evaluate a three-leaf Kadeishvili tree for the inclusion i on three elementary polygons surrounding a common puncture (for the three-holed sphere with its standard arc system) and compare to the genuine μ≥3 value on the resulting disk sequence; any nonzero difference disproves Lemma 4.7 and Theorem 4.13(1).

Watch

Extended reading notes

Core claim

The paper establishes a two-step procedure that computes minimal models of 'spectral DGLAs', i.e. DGLAs written as a twisting (V, d0+[W,−],[−,−]) of a simpler DGLA by an almost-pronilpotent Maurer-Cartan element W. One takes the minimal model of the untwisted DGLA, twists it by the image of W, and takes the minimal model again; the resulting composite inclusion back into the original twisted DGLA is the candidate quasi-isomorphism. The main theorem, for the A∞-gentle algebra of a punctured surface, says this composite is an L∞-quasi-isomorphism: the Hochschild complex is L∞-quasi-isomorphic to its cohomology, so Hochschild cohomology is formal and the transfer is explicit. The paper also mat

Load-bearing premise

The load-bearing premise is that the Maurer-Cartan element WH formed from polygon data maps under the minimal-model inclusion exactly to the genuine higher products μ≥3 of the gentle category; the paper checks agreement on elementary polygons and asserts that all multi-polygon corrections already lie in the known part of μ≥3, so any correction landing outside that part would make the whole construction compute the wrong complex.

Editorial extensions

If this is right

For a minimal A∞-category C, the Hochschild DGLA is a spectral DGLA with W=μ≥3, so the two-step procedure applies whenever the classical Hochschild cohomology of the underlying associative category is computable.
The L∞-quasi-isomorphism of Theorem 4.13(1) proves formality of HH(GtlΣ) and gives an explicit transfer from the Hochschild complex to its cohomology, replacing the earlier grading-based formality argument.
All statements survive tensoring with the maximal ideal of a deformation base (Theorem 4.13(2)), so deformations of the gentle algebra are controlled by the parameter space V in a Maurer-Cartan-preserving way.
The same strategy is suggested for other twisted DGLAs, such as the Landau-Ginzburg Hochschild cohomology of dimer models, where only the cohomology vector space was previously computed.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The method is plausibly general: if the identification of WH with μ≥3 can be verified for other minimal A∞-categories, the entire L∞-structure on their Hochschild cohomology would follow from classical associative Hochschild data without successive one-page-at-a-time transfers.
In filtered settings where the higher structure is not MC-twisted, the paper's 'degeneration on the second page' suggests a direct route to comparing deformation functors of the twisted and untwisted objects by one quasi-isomorphism.
A constructive check of Lemma 4.7 for a small surface (e.g., the three-holed sphere with its standard arc system) via computer algebra would either certify the main theorem or exhibit the explicit obstruction; this is testable with the given cocycle formulas.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's my read. The genuinely new thing is the spectral-DGLA formalism: twisting a DGLA by an almost pronilpotent Maurer-Cartan element, then using the embraced inclusion i_WH to get a two-step minimal model that preserves L∞ structure. The idea of viewing the Hochschild complex of a minimal A∞-category as the twisting of the associative Hochschild complex by μ≥3 is clean and probably transferable. The bracket computations in Lemma 4.6 are detailed and mostly careful, including the convergence argument for infinite series. Credit where due.

But the application has a load-bearing gap. Lemma 4.7 is the step that identifies i_MC(W_H) with μ≥3. The third part of its proof asserts that two MC elements supported on disk sequences that agree on elementary polygons must agree everywhere. That doesn't follow from the MC equation alone; you need to prove a recursive generation statement showing the h-decorated Kadeishvili trees don't change the coefficients on non-elementary disks. The stress-test note is right. This is not a fatal flaw in the sense that the result is already known from [4], and the bracket computations are independent. But as a proof of the spectral inclusion theorem, it's incomplete.

That isn't the only soft spot. Lemma 3.3 explicitly omits sign checks, and Lemma 4.2 shortens everything to ±. For a paper whose machinery is about signs in L∞-algebras, that's uncomfortable, even if the final result is plausible. Theorem 4.13's proof also invokes [4,12] for the identification of the image instead of carrying out the promised trace, so the main theorem leans on the very result it recovers. The paper honestly flags the anticipation in [2] and its own errors; that's in its favor.

Still, the framework is worth engaging with. The paper writes out the homological splitting and the brackets in real detail, and the second page of this spectral DGLA is genuinely different from the classical transfer story. I'd send it to a serious referee. A referee can demand a full proof of Lemma 4.7 and a sign audit. The result itself likely survives.

Referee Report

3 major / 6 minor

Summary. The paper proposes a method to compute minimal models of DGLAs presented as twistings by almost pronilpotent Maurer–Cartan elements: instead of transferring structure page by page, one transfers the twisting element to cohomology and then studies the twisted minimal model. The method is applied to Hochschild cohomology of minimal A∞-categories, where the A∞-structure μ = μ2 + μ≥3 presents HC(C) as HC(C2)_{μ≥3}. For gentle algebras GtlΣ, the paper chooses an explicit Maurer–Cartan element WH in HH(Gtl2Σ), computes brackets in HH(Gtl2Σ) and in HH(Gtl2Σ)_{WH}, and claims in Theorem 4.13 that the composite spectral inclusion is an L∞-quasi-isomorphism, recovering the formality result of [4] and giving an explicit L∞-quasi-isomorphism between HC(GtlΣ) and its cohomology.

Significance. If the main theorem is correct, the paper provides a conceptually clean and somewhat more explicit proof of formality of Hochschild cohomology of A∞-gentle algebras, together with an explicit L∞-quasi-isomorphism between the Hochschild complex and its cohomology. The general twisting/minimal-model strategy is interesting and may apply to other DGLAs. The paper contains a substantial amount of explicit combinatorics: definitions of auxiliary cochains, computations of Gerstenhaber brackets, and a proposed homological splitting. However, the central application depends on an unproven identification in Lemma 4.7 and on representatives imported from [4,12], so the contribution is conditional rather than self-contained. The paper does not provide machine-checked proofs or code.

major comments (3)

[§4.2, Lemma 4.7] The third step of the proof is the load-bearing step: it asserts that iMC(WH) = μ≥3 because both are Maurer–Cartan elements in HC(Gtl2Σ), agree on elementary polygons, and are supported on disk sequences. This inference is not justified. The Maurer–Cartan equation imposes relations but does not determine an A∞-structure by its values on elementary polygons. The second step only shows that tree contributions with at least two leaves lie, up to sign and weight, in the subspace spanned by cochains attached to non-elementary disk sequences; it does not show that the coefficients coincide with the specific μ≥3 of Definition 2.14. Since the equality iMC(WH)=μ≥3 is what identifies the twisting element used in the spectral inclusion, a gap here undermines Theorem 4.13(1). A direct coefficient-by-coefficient computation on non-elementary disk sequences is needed.
[§4.4, Theorem 4.13] The proof of statement (1) consists of the sentence that the composite sends cohomology basis elements to 'the standard Hochschild cohomology representatives in HC(GtlΣ) constructed in [4,12]'. This does not establish that the composite is a quasi-isomorphism: one must check that these representatives are cohomologous to a basis of HH(GtlΣ) and that the map is surjective on cohomology, or otherwise prove the cohomology of the target is isomorphic to the stated H. The reference to [4,12] is also a reliance on the very results the paper aims to recover or make explicit. Remark 4.11 explicitly says that for gentle algebras the map is checked 'with the help of the description of Hochschild cohomology from [4]', but the manuscript does not specify which part of the check is carried out here versus imported. This needs to be clarified and the missing cohomological verification supplied.
[§3.1, Lemma 3.3] The proof of Lemma 3.3 concludes 'We omit sign checks and finish the proof.' The twisting formulas for morphisms and the transport of Maurer–Cartan elements are used throughout the paper, and the L∞-morphism relations are sign-sensitive. Since the paper's main claims are formulated in terms of L∞-quasi-isomorphisms, signs are load-bearing. The proof should either include the sign checks or cite a source where the result is proven with compatible conventions and state explicitly that the omitted signs are verified.

minor comments (6)

[§4.2, Lemma 4.7] The notation 'μ≥3≥2' is confusing; the intended splitting μ≥3 = μ≥3_1 + μ≥3_{≥2} should be defined explicitly and used consistently.
[§4.2, Lemma 4.6] The bracket [νB,k,o, νB′,k′,o] is dismissed as 'very similar to Lemma 4.5'. Since this bracket is used to argue that higher brackets vanish, a few details or a precise reference to the computation would improve verifiability.
[§4.1, Lemma 4.2] In types F and G, the proof says 'This case is similar to case F' and 'Analogous reasoning shows'; these cases are nontrivial and should be written out in the same detail as the other types.
[§2.1, Lemma 2.16] The sign computations rely on congruences such as 'We have used that ∥βi∥+...+∥βi+kl−2∥ ≡ ∥βi−1∥' and '∥βiγ∥+...+∥βi+kl−1∥ = |γ|' without derivation. These should be justified or replaced by an explicit grading check.
[References] Reference [16] has incomplete bibliographic data; it should include authors and full title/page details. Several other references to the author's own arXiv papers would benefit from publication status if known.
[§4.4, Theorem 4.13(2)] The claim that a quasi-isomorphism remains a quasi-isomorphism after tensoring with the maximal ideal of a deformation base should state the required nilpotence/completeness condition explicitly, or cite the exact result used.

Circularity Check

2 steps flagged · score 6.0 of 10

Main quasi-isomorphism is checked via self-citations [4,12] and Lemma 4.7 asserts the key Maurer-Cartan identification, so the recovery of formality is only partially independent.

self citation load bearing [Remark 4.11 and proof of Theorem 4.13(1), Section 4.4]
"For gentle algebras, we are however able to check this by hand with the help of the description of Hochschild cohomology from [4]. In result, the description of the entire L∞-structure on HH(GtlΣ) including the vanishing of the higher brackets is immediate."

The central claim Theorem 4.13(1) is that the spectral inclusion is a quasi-isomorphism, which implies formality of HH(GtlΣ). The proof does not compute the relevant cohomology internally; it says the images are 'the standard Hochschild cohomology representatives in HC(GtlΣ) constructed in [4,12]' and Remark 4.11 explicitly says the quasi-isomorphism was checked using [4]'s description of Hochschild cohomology. Since [4] is Bocklandt–van de Kreeke, the same authors' prior paper whose formality result the present paper claims to recover, the verification of the main theorem is load-bearing on a self-citation. Removing [4,12] would leave the spectral inclusion unproven as a quasi-isomorphism.
other [Lemma 4.7, Section 4.2, proof step 3]
"Since they agree on elementary polygons and only take values on disk sequences, instead of arbitrary angle sequences, we conclude that iMC(WH ) = µ≥3."

Lemma 4.7's conclusion is exactly iMC(WH)=μ≥3. The preceding step only shows that tree contributions with at least two leaves produce cochains that, 'up to sign and weight factor, already lie in μ≥3≥2'; it does not compute the coefficients or show they match the specific higher products of Definition 2.14. The final step then asserts that because both sides are Maurer-Cartan elements agreeing on elementary polygons and supported on disk sequences, they agree everywhere. This is an unproven uniqueness claim: the Maurer-Cartan equation does not by itself determine a disk-sequence-supported A∞-structure from its elementary-polygon components. Thus the proof assumes the missing coefficient equality, i.e. the lemma's conclusion, rather than deriving it.

full rationale

Sections 3.1–3.3 develop a general L∞-transfer/twisting framework that is self-contained and does not reduce to prior work: Lemma 3.2, Lemma 3.3, Lemma 3.6 and Lemma 3.7 are independent homological-algebra statements. The bracket computations in Lemma 4.6 are also carried out directly inside the paper. However, the application to gentle algebras is where circularity enters. The identification of the chosen Maurer-Cartan element WH with the true higher products μ≥3 (Lemma 4.7) is asserted through an invalid uniqueness inference rather than proven by explicit coefficient comparison; this is an omitted proof that is load-bearing for the spectral inclusion. Moreover, the proof of the main quasi-isomorphism and the verification of the whole L∞-structure are explicitly delegated to the same authors' earlier work [4,12]. Because the paper's stated goal is to 'recover' the formality result of [4], using [4] as the check for the central quasi-isomorphism makes the recovery partially circular. The paper is not entirely circular—the L∞-spectral machinery and many bracket computations are new and independent—but the headline application depends on self-citation and on an unproven matching step, so a score of 6 is appropriate.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper builds on previous constructions of gentle algebras and their Hochschild cohomology from [2,3,4], and on standard homological perturbation theory. The main additional choices are the homological splitting R and the sporadic set Sgeneric, imported from prior work. No new particles, forces, or empirical entities are postulated.

free parameters (3)

Generic sporadic set Sgeneric = |M|+1 functions, chosen precisely so cocycles form a basis
Chosen from [2]; its cardinality is |M|+1. The paper does not derive it; it is an input from prior literature on which the basis of HH(Gtl2Σ) depends.
Choice of complement R in homological splitting = any complement with Rpart ⊆ R
Definition 4.3. The Kadeishvili minimal model and the brackets in Lemma 4.6 depend on this choice. Existence depends on Lemma 4.2.
Distinguished polygon B0 excluded from Spoly = one elementary polygon
Lemma 4.9 uses B0 to handle the polygon sporadic class νB,1,o; the choice affects the formulas but not the brackets.

assumptions (4)

standard math Homological perturbation theory / Kadeishvili minimal model construction for L∞-algebras
Theorem 2.9 is quoted without proof; it underpins the entire strategy and the computation of i_MC(WH).
domain assumption Description of HH(Gtl2Σ) in Z/2Z grading via νλ, νB, νq,k,o, νB,k,e
Theorem 2.17 is quoted from [2]; the whole splitting H in Definition 4.3 uses this basis.
domain assumption The A∞-structure μ of GtlΣ is the twisting by μ≥3 and satisfies the A∞ relations
Definitions 2.13-2.14 from [3,4]; the paper checks only cocycle conditions for νB,k,o/e, not that μ satisfies all A∞ relations.
ad hoc to paper Sgeneric exists and is chosen from [2] with the right additivity and vanishing properties
Section 2.3: 'The set Sgeneric is chosen precisely so that the cocycles νλ, νB and νq,k,o together form a basis'. This is an external choice.

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Cite this review

Pith. "Pith review of $ L_\infty $-spectral sequences for Hochschild cohomology." pith.science (2026). https://pith.science/paper/JOLGJBXX

@misc{pith2026250821716,
  author       = {Pith},
  title        = {Pith review of: $ L_\infty $-spectral sequences for Hochschild cohomology},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JOLGJBXX}},
  note         = {Machine review of arXiv:2508.21716}
}

abstract

Spectral sequences are a common tool to compute cohomology spaces, but higher structure is often lost on the way. In this article we exhibit a strategy to retain the higher structure on the cohomology, which works in case the chain complex with higher structure is presented as the twisting of a simpler chain complex by a Maurer-Cartan element. This works particularly well in case of the Hochschild complex of a minimal $ A_\infty $-category, where the Hochschild complex can be seen as the twisting of the Hochschild complex of the underlying associative algebra or category. As an application, we recover the existing formality result for Hochschild cohomology of wrapped Fukaya categories of punctured surfaces, and provide an $ L_\infty $-quasi-isomorphism between the Hochschild complex and its cohomology.

Figures

Figures reproduced from arXiv: 2508.21716 by the authors.

**Figure 2.1.** Degree of an angle α in Gtl2 Σ 3 2 2 1 1 5 5 4 4 3 (a) Standard polygon P5 (b) A disk sequence (c) Not a disk sequence [PITH_FULL_IMAGE:figures/full_fig_p006_2_1.png] view at source ↗

**Figure 2.2.** Illustration of immersed disks We are now ready to recall the construction of the category Gtl2 Σ. Let (Σ, M) be a punctured surface and A be a full arc system for Σ which satisfies [NMD]. The classical gentle algebra Gtl2 Σ is a graded associative category defined as follows. Its objects are the arcs a ∈ A. A basis for the hom space HomGtl2 Σ(a, b) is given by the set of all angles around punctures from a to b. Thi… view at source ↗

**Figure 4.1.** This figure illustrates how the differential [PITH_FULL_IMAGE:figures/full_fig_p013_4_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

18 extracted references · 12 canonical work pages

[4]

Deformations of Gentle $A_\infty$-Algebras

Raf Bocklandt and Jasper van de Kreeke. Deformations of Gentle A∞-Algebras. 2023. eprint: arXiv:2304.10223

work page Pith review arXiv 2023
[2]

A gentle introduction to homological mirror symmetry

Raf Bocklandt. A gentle introduction to homological mirror symmetry . Vol. 99. London Mathematical Society Student Texts. Cambridge University Press, Cambridge, 2021, pp. xi+390. isbn: 978-1-108-48350-6; 978-1-108-72875-1. doi: 10.1017/9781108692458

doi:10.1017/9781108692458 2021
[1]

Deformations of path algebras of quivers with re- lations

Severin Barmeier and Zhengfang Wang. Deformations of path algebras of quivers with re- lations. 2020. eprint: arXiv:2002.10001

arXiv 2020
[3]

Noncommutative mirror symmetry for punctured surfaces

Raf Bocklandt. “Noncommutative mirror symmetry for punctured surfaces”. In: T rans. Amer. Math. Soc. 368.1 (2016). With an appendix by Mohammed Abouzaid, pp. 429–469

work page 2016
[5]

Projective resolutions of associative algebras and ambiguities

Sergio Chouhy and Andrea Solotar. “Projective resolutions of associative algebras and ambiguities”. In: J. Algebra 432 (2015), pp. 22–61. issn: 0021-8693,1090-266X. doi: 10.1016/j.jalgebra. 2015.02.019. url: https://doi.org/10.1016/j.jalgebra.2015.02.019

doi:10.1016/j.jalgebra 2015
[6]

Filtered A-infinity structures in complex geometry

Joana Cirici and Anna Sopena-Gilboy. “Filtered A-infinity structures in complex geometry”. In: Proc. Amer. Math. Soc. 150.9 (2022), pp. 4067–4082. issn: 0002-9939,1088-6826. doi: 10.1090/ proc/16009. url: https://doi.org/10.1090/proc/16009

work page doi:10.1090/proc/16009 2022
[7]

Higher holonomy for curved L∞-algebras 1: simplicial methods

Ezra Getzler. Higher holonomy for curved L∞-algebras 1: simplicial methods. 2025. arXiv: 2408.11157 [math.AT]. url: https://arxiv.org/abs/2408.11157

arXiv 2025
[8]

Flat surfaces and stability structures

F. Haiden, L. Katzarkov, and M. Kontsevich. “Flat surfaces and stability structures”. In: Publ. Math. Inst. Hautes ´Etudes Sci. 126 (2017), pp. 247–318. 20

work page 2017

Show all 18 references

[9]

A-infinity-algebras, spectral sequences and exact couples

Estanislao Herscovich. A-infinity-algebras, spectral sequences and exact couples . 2014. arXiv: 1410.6728 [math.KT]. url: https://arxiv.org/abs/1410.6728

2014 arXiv
[10]

Deformation quantization of Poisson manifolds

Maxim Kontsevich. “Deformation quantization of Poisson manifolds”. In: Lett. Math. Phys. 66.3 (2003), pp. 157–216. issn: 0377-9017,1573-0530. doi: 10.1023/B:MATH.0000027508.00421.bf . url: https://doi.org/10.1023/B:MATH.0000027508.00421.bf

2003
[11]

A∞-Deformations and their Derived Categories

Jasper van de Kreeke. A∞-Deformations and their Derived Categories . 2023. arXiv: 2308. 08026 [math.KT]. url: https://arxiv.org/abs/2308.08026

2023 arXiv
[12]

Explicit Hochschild Cocycles for Gentle Algebras

Jasper van de Kreeke. Explicit Hochschild Cocycles for Gentle Algebras. 2023. arXiv: 2308. 09533 [math.RA]. url: https://arxiv.org/abs/2308.09533

2023 arXiv
[13]

Relative F ukaya Categories via Gentle Algebras

Jasper van de Kreeke. Relative F ukaya Categories via Gentle Algebras. 2023. eprint: arXiv: 2305.09112

2023 arXiv
[14]

Deformation theory via differential graded Lie algebras

Marco Manetti. Deformation theory via differential graded Lie algebras. 2005. arXiv: math/ 0507284 [math.AG]. url: https://arxiv.org/abs/math/0507284

2005 arXiv
[15]

The controlling L ∞-algebra, cohomology and homotopy of embedding tensors and Lie-Leibniz triples

Yunhe Sheng, Rong Tang, and Chenchang Zhu. “The controlling L ∞-algebra, cohomology and homotopy of embedding tensors and Lie-Leibniz triples”. In:Communications in Mathematical Physics Volume 386, Issue 1 (), pp. 269–304
[16]

The Alternating Syzygy Behavior of Monomial Algebras

“The Alternating Syzygy Behavior of Monomial Algebras”. In: Journal of Algebra 188 (1997), pp. 69–89

1997
[17]

Dimer models and Hochschild cohomology

Michael Wong. “Dimer models and Hochschild cohomology”. In: J. Algebra 585 (2021), pp. 207–

2021
[279]

doi: 10.1016/j.jalgebra.2021.06.003

issn: 0021-8693. doi: 10.1016/j.jalgebra.2021.06.003. Department of Mathematics, University of California, Berkeley, USA jasper.kreeke@berkeley.edu 21

2021 doi

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [4]

Deformations of Gentle $A_\infty$-Algebras

Raf Bocklandt and Jasper van de Kreeke. Deformations of Gentle A∞-Algebras. 2023. eprint: arXiv:2304.10223

work page Pith review arXiv 2023

[2] [2]

A gentle introduction to homological mirror symmetry

Raf Bocklandt. A gentle introduction to homological mirror symmetry . Vol. 99. London Mathematical Society Student Texts. Cambridge University Press, Cambridge, 2021, pp. xi+390. isbn: 978-1-108-48350-6; 978-1-108-72875-1. doi: 10.1017/9781108692458

doi:10.1017/9781108692458 2021

[3] [1]

Deformations of path algebras of quivers with re- lations

Severin Barmeier and Zhengfang Wang. Deformations of path algebras of quivers with re- lations. 2020. eprint: arXiv:2002.10001

arXiv 2020

[4] [3]

Noncommutative mirror symmetry for punctured surfaces

Raf Bocklandt. “Noncommutative mirror symmetry for punctured surfaces”. In: T rans. Amer. Math. Soc. 368.1 (2016). With an appendix by Mohammed Abouzaid, pp. 429–469

work page 2016

[5] [5]

Projective resolutions of associative algebras and ambiguities

Sergio Chouhy and Andrea Solotar. “Projective resolutions of associative algebras and ambiguities”. In: J. Algebra 432 (2015), pp. 22–61. issn: 0021-8693,1090-266X. doi: 10.1016/j.jalgebra. 2015.02.019. url: https://doi.org/10.1016/j.jalgebra.2015.02.019

doi:10.1016/j.jalgebra 2015

[6] [6]

Filtered A-infinity structures in complex geometry

Joana Cirici and Anna Sopena-Gilboy. “Filtered A-infinity structures in complex geometry”. In: Proc. Amer. Math. Soc. 150.9 (2022), pp. 4067–4082. issn: 0002-9939,1088-6826. doi: 10.1090/ proc/16009. url: https://doi.org/10.1090/proc/16009

work page doi:10.1090/proc/16009 2022

[7] [7]

Higher holonomy for curved L∞-algebras 1: simplicial methods

Ezra Getzler. Higher holonomy for curved L∞-algebras 1: simplicial methods. 2025. arXiv: 2408.11157 [math.AT]. url: https://arxiv.org/abs/2408.11157

arXiv 2025

[8] [8]

Flat surfaces and stability structures

F. Haiden, L. Katzarkov, and M. Kontsevich. “Flat surfaces and stability structures”. In: Publ. Math. Inst. Hautes ´Etudes Sci. 126 (2017), pp. 247–318. 20

work page 2017