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Invariant splitting principles for the Lipshitz--Ozsv\'ath--Thurston correspondence

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arxiv 2404.06618 v2 pith:N4RDEDD5 submitted 2024-04-09 math.GT

Gary Guth , Sungkyung Kang This is my paper · ORCID
classification math.GT
keywords floerknothomologyinvariantborderedcomplementscomplexescorrespondence
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abstract

We prove that the Lipshitz-Ozsv\'ath-Thurston correspondence between extended type D structures of knot complements and $\mathbb{F}[U, V]/(UV)$ knot Floer complexes can be arranged so that $\iota_K$-invariant splittings of knot Floer chain complexes correspond to $\iota_{S^3 \setminus K}$-invariant splittings of bordered Floer homology of knot complements. For patterns satisfying the satellite extension property, which include cabling patterns, this provides a novel way to compute the involutive knot Floer homology of satellites from that of their companions. As a topological application, we show that our results can be applied to construct infinitely many examples of exotic pairs of contractible 4-manifolds which remain exotic after one stabilization. Along the way, we also establish first order naturality of bordered Floer homology.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Naturality in real Heegaard Floer theory

    math.GT 2026-07 conditional novelty 7.0 of 10

    Real Heegaard Floer homology becomes a natural functor on based real 3-manifolds, with an equivariant mapping class group action and a new involutive variant.

  2. Satellites and telescopes: a concordance formula for bordered Floer homology

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    Locally symmetric endomorphisms of the knot Floer complex correspond, up to a canonical class theta^-_K, to type-D endomorphisms of the bordered complement, making satellite concordance maps combinatorially computable.

  3. The link surgery formula and equivariant surgeries

    math.GT 2025-07 conditional novelty 7.0 of 10

    An equivariant link surgery formula is proved, giving diffeomorphism-induced maps on Heegaard Floer homology, and used to show the kernel of the forgetful map from the equivariant homology cobordism group contains a Z...

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    math.GT 2026-01 conditional novelty 6.0 of 10

    The boundaries of the AKMR and Tange cork families, and nontrivial equivariant connected sums of them, are strong corks.

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