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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2110.03082 |
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| _version_ | 1866917945753468928 |
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| author | Boninger, Joe |
| author_facet | Boninger, Joe |
| contents | We give an explicit algorithm for calculating the Kauffman bracket of a link diagram from a Goeritz matrix for that link. Further, we show how the Jones polynomial can be recovered from a Goeritz matrix when the corresponding checkerboard surface is orientable, or when more information is known about its Gordon-Litherland form. In the process we develop a theory of Goeritz matrices for cographic matroids, which extends the bracket polynomial to any symmetric integer matrix. We place this work in the context of links in thickened surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_03082 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Jones Polynomial from a Goeritz Matrix Boninger, Joe Geometric Topology 57K14, 05B35 We give an explicit algorithm for calculating the Kauffman bracket of a link diagram from a Goeritz matrix for that link. Further, we show how the Jones polynomial can be recovered from a Goeritz matrix when the corresponding checkerboard surface is orientable, or when more information is known about its Gordon-Litherland form. In the process we develop a theory of Goeritz matrices for cographic matroids, which extends the bracket polynomial to any symmetric integer matrix. We place this work in the context of links in thickened surfaces. |
| title | The Jones Polynomial from a Goeritz Matrix |
| topic | Geometric Topology 57K14, 05B35 |
| url | https://arxiv.org/abs/2110.03082 |