Cobordism maps in Khovanov homology and singular instanton homology I
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908828261416960 |
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| author | Imori, Hayato Sano, Taketo Sato, Kouki Taniguchi, Masaki |
| author_facet | Imori, Hayato Sano, Taketo Sato, Kouki Taniguchi, Masaki |
| contents | Khovanov homology and singular instanton Floer homology are both functorial with respect to link cobordisms. Although the two homology groups are related by a spectral sequence, direct correspondence between the cobordism maps has not been rigorously established. In this paper, we define a cobordism map on the instanton cube complex as a filtered chain map, and prove that it recovers the cobordism maps both in Khovanov homology and singular instanton theory. In a sequel paper, we further extend this cobordism map to immersed cobordisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12095 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cobordism maps in Khovanov homology and singular instanton homology I Imori, Hayato Sano, Taketo Sato, Kouki Taniguchi, Masaki Geometric Topology 57K18 57R58 Khovanov homology and singular instanton Floer homology are both functorial with respect to link cobordisms. Although the two homology groups are related by a spectral sequence, direct correspondence between the cobordism maps has not been rigorously established. In this paper, we define a cobordism map on the instanton cube complex as a filtered chain map, and prove that it recovers the cobordism maps both in Khovanov homology and singular instanton theory. In a sequel paper, we further extend this cobordism map to immersed cobordisms. |
| title | Cobordism maps in Khovanov homology and singular instanton homology I |
| topic | Geometric Topology 57K18 57R58 |
| url | https://arxiv.org/abs/2505.12095 |