Knot Floer homology, link Floer homology and link detection
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866910383259779072 |
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| author | Binns, Fraser Martin, Gage |
| author_facet | Binns, Fraser Martin, Gage |
| contents | We give new link detection results for knot and link Floer homology inspired by recent work on Khovanov homology. We show that knot Floer homology detects $T(2,4)$, $T(2,6)$, $T(3,3)$, $L7n1$, and the link $T(2,2n)$ with the orientation of one component reversed. We show link Floer homology detects $T(2,2n)$ and $T(n,n)$, for all $n$. Additionally we identify infinitely many pairs of links such that both links in the pair are each detected by link Floer homology but have the same Khovanov homology and knot Floer homology. Finally, we use some of our knot Floer detection results to give topological applications of annular Khovanov homology. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2011_02005 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Knot Floer homology, link Floer homology and link detection Binns, Fraser Martin, Gage Geometric Topology 57K18, 57K10 We give new link detection results for knot and link Floer homology inspired by recent work on Khovanov homology. We show that knot Floer homology detects $T(2,4)$, $T(2,6)$, $T(3,3)$, $L7n1$, and the link $T(2,2n)$ with the orientation of one component reversed. We show link Floer homology detects $T(2,2n)$ and $T(n,n)$, for all $n$. Additionally we identify infinitely many pairs of links such that both links in the pair are each detected by link Floer homology but have the same Khovanov homology and knot Floer homology. Finally, we use some of our knot Floer detection results to give topological applications of annular Khovanov homology. |
| title | Knot Floer homology, link Floer homology and link detection |
| topic | Geometric Topology 57K18, 57K10 |
| url | https://arxiv.org/abs/2011.02005 |