Invariant splitting principles for the Lipshitz--Ozsváth--Thurston correspondence

Gary Guth; Sungkyung Kang

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arXiv · 2404.06618

Invariant splitting principles for the Lipshitz--Ozsváth--Thurston correspondence

Gary Guth·Sungkyung Kang

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Abstract

We prove that the Lipshitz-Ozsváth-Thurston correspondence between extended type D structures of knot complements and $\mathbb{F}[U, V]/(UV)$ knot Floer complexes can be arranged so that $ι_K$-invariant splittings of knot Floer chain complexes correspond to $ι_{S^3 \setminus K}$-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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BibTeX RIS

Gary Guth, Sungkyung Kang. 2026-07-31. Invariant splitting principles for the Lipshitz--Ozsváth--Thurston correspondence. https://arxiv.org/abs/2404.06618

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