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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.06618 |
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| _version_ | 1866913308422963200 |
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| author | Guth, Gary Kang, Sungkyung |
| author_facet | Guth, Gary Kang, Sungkyung |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06618 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invariant splitting principles for the Lipshitz--Ozsváth--Thurston correspondence Guth, Gary Kang, Sungkyung Geometric Topology 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. |
| title | Invariant splitting principles for the Lipshitz--Ozsváth--Thurston correspondence |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2404.06618 |