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Bibliographic Details
Main Authors: Guth, Gary, Kang, Sungkyung
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2404.06618
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Table of Contents:
  • 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.