An Ozsváth--Szabó-type spectral sequence for links in $S^1\times S^2$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909137729748992 |
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| author | Cohen, Jesse |
| author_facet | Cohen, Jesse |
| contents | We show that there is a spectral sequence with $E^2$-page given by the Khovanov homology of a link in $S^1\times S^2$, as defined by Rozansky in arXiv:1011.1958, which converges to the Hochschild homology of an $A_\infty$-bimodule defined in terms of bordered Floer invariants. We also show that the homology algebras $H_*\mathfrak{h}_n$ of the algebras $\mathfrak{h}_n$ over which these bimodules are defined give nontrivial $A_\infty$-deformations of Khovanov's arc algebras $H_n$ for $n>1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09790 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Ozsváth--Szabó-type spectral sequence for links in $S^1\times S^2$ Cohen, Jesse Geometric Topology 57K18 (primary) 57R58, 57M12 (secondary) We show that there is a spectral sequence with $E^2$-page given by the Khovanov homology of a link in $S^1\times S^2$, as defined by Rozansky in arXiv:1011.1958, which converges to the Hochschild homology of an $A_\infty$-bimodule defined in terms of bordered Floer invariants. We also show that the homology algebras $H_*\mathfrak{h}_n$ of the algebras $\mathfrak{h}_n$ over which these bimodules are defined give nontrivial $A_\infty$-deformations of Khovanov's arc algebras $H_n$ for $n>1$. |
| title | An Ozsváth--Szabó-type spectral sequence for links in $S^1\times S^2$ |
| topic | Geometric Topology 57K18 (primary) 57R58, 57M12 (secondary) |
| url | https://arxiv.org/abs/2403.09790 |