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

2024/04/09 by Guth, Gary, Kang, Sungkyung
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2404.06618

Abstract

We prove that the Lipshitz-Ozsváth-Thurston correspondence between extended type D structures of knot complements and \mathbbF[U, V]/(UV) knot Floer complexes can be arranged so that ι_K-invariant splittings of knot Floer chain complexes correspond to ι_{S³ ∖ 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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