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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.11109 |
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| _version_ | 1866908428996182016 |
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| author | Li, Zhenkun Xie, Yi Zhang, Boyu |
| author_facet | Li, Zhenkun Xie, Yi Zhang, Boyu |
| contents | We define a 1-parameter family of homology invariants for links in thickened oriented surfaces. It recovers the homology invariant of Asaeda-Przytycki-Sikora (arxiv:0409414) and the invariant defined by Winkeler (arxiv:2106.03834). The new invariant can be regarded as a deformation of Asaeda-Przytycki-Sikora homology; it is not a Lee-type deformation as the deformation is only non-trivial when the surface is not simply connected. Our construction is motivated by computations in singular instanton Floer homology. We also prove a detection property for the new invariant, which is a stronger result than the main theorem of arxiv:2208.13963. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_11109 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A deformation of Asaeda-Przytycki-Sikora homology Li, Zhenkun Xie, Yi Zhang, Boyu Geometric Topology 57K18 We define a 1-parameter family of homology invariants for links in thickened oriented surfaces. It recovers the homology invariant of Asaeda-Przytycki-Sikora (arxiv:0409414) and the invariant defined by Winkeler (arxiv:2106.03834). The new invariant can be regarded as a deformation of Asaeda-Przytycki-Sikora homology; it is not a Lee-type deformation as the deformation is only non-trivial when the surface is not simply connected. Our construction is motivated by computations in singular instanton Floer homology. We also prove a detection property for the new invariant, which is a stronger result than the main theorem of arxiv:2208.13963. |
| title | A deformation of Asaeda-Przytycki-Sikora homology |
| topic | Geometric Topology 57K18 |
| url | https://arxiv.org/abs/2302.11109 |