Homology concordance and knot Floer homology
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866909301585477632 |
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| author | Dai, Irving Hom, Jennifer Stoffregen, Matthew Truong, Linh |
| author_facet | Dai, Irving Hom, Jennifer Stoffregen, Matthew Truong, Linh |
| contents | We study the homology concordance group of knots in integer homology three-spheres which bound integer homology four-balls. Using knot Floer homology, we construct an infinite number of $\mathbb{Z}$-valued, linearly independent homology concordance homomorphisms which vanish for knots coming from $S^3$. This shows that the homology concordance group modulo knots coming from $S^3$ contains an infinite-rank summand. The techniques used here generalize the classification program established in previous papers regarding the local equivalence group of knot Floer complexes over $\mathbb{F}[U, V]/(UV)$. Our results extend this approach to complexes defined over a broader class of rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_14803 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Homology concordance and knot Floer homology Dai, Irving Hom, Jennifer Stoffregen, Matthew Truong, Linh Geometric Topology 57M25, 57N70, 57R58 We study the homology concordance group of knots in integer homology three-spheres which bound integer homology four-balls. Using knot Floer homology, we construct an infinite number of $\mathbb{Z}$-valued, linearly independent homology concordance homomorphisms which vanish for knots coming from $S^3$. This shows that the homology concordance group modulo knots coming from $S^3$ contains an infinite-rank summand. The techniques used here generalize the classification program established in previous papers regarding the local equivalence group of knot Floer complexes over $\mathbb{F}[U, V]/(UV)$. Our results extend this approach to complexes defined over a broader class of rings. |
| title | Homology concordance and knot Floer homology |
| topic | Geometric Topology 57M25, 57N70, 57R58 |
| url | https://arxiv.org/abs/2110.14803 |