Real monopoles and a spectral sequence from Khovanov homology
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909214575689728 |
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| author | Li, Jiakai |
| author_facet | Li, Jiakai |
| contents | Given a based link $(K,p)$, we define a "tilde"-version $\tilde{HMR}(K,p)$ of real monopole Floer homology and prove an unoriented skein exact triangle. We show the Euler characteristic of $\tilde{HMR}(K,p)$ is equal to Miyazawa's invariant $|deg(K)|$ arXiv:2312.02041 and examine some examples. Further, we construct a spectral sequence over $\mathbb{F}_2$ abutting to $\tilde{HMR}(K,p)$, whose $E_2$ page is the reduced Khovanov homology $Khr(\overline{K})$ of the mirror link $\overline{K}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00152 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Real monopoles and a spectral sequence from Khovanov homology Li, Jiakai Geometric Topology 57R58, 57M25, 57K18 Given a based link $(K,p)$, we define a "tilde"-version $\tilde{HMR}(K,p)$ of real monopole Floer homology and prove an unoriented skein exact triangle. We show the Euler characteristic of $\tilde{HMR}(K,p)$ is equal to Miyazawa's invariant $|deg(K)|$ arXiv:2312.02041 and examine some examples. Further, we construct a spectral sequence over $\mathbb{F}_2$ abutting to $\tilde{HMR}(K,p)$, whose $E_2$ page is the reduced Khovanov homology $Khr(\overline{K})$ of the mirror link $\overline{K}$. |
| title | Real monopoles and a spectral sequence from Khovanov homology |
| topic | Geometric Topology 57R58, 57M25, 57K18 |
| url | https://arxiv.org/abs/2406.00152 |