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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2010.08499 |
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| _version_ | 1866908354556723200 |
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| author | Champanerkar, Abhijit Kofman, Ilya |
| author_facet | Champanerkar, Abhijit Kofman, Ilya |
| contents | Dasbach and Lin proved a "volumish theorem" for alternating links. We prove the analogue for alternating link diagrams on surfaces, which provides bounds on the hyperbolic volume of a link in a thickened surface in terms of coefficients of its reduced Jones-Krushkal polynomial. Along the way, we show that certain coefficients of the 4-variable Krushkal polynomial express the cycle rank of the reduced Tait graph on the surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_08499 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A volumish theorem for alternating virtual links Champanerkar, Abhijit Kofman, Ilya Geometric Topology Dasbach and Lin proved a "volumish theorem" for alternating links. We prove the analogue for alternating link diagrams on surfaces, which provides bounds on the hyperbolic volume of a link in a thickened surface in terms of coefficients of its reduced Jones-Krushkal polynomial. Along the way, we show that certain coefficients of the 4-variable Krushkal polynomial express the cycle rank of the reduced Tait graph on the surface. |
| title | A volumish theorem for alternating virtual links |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2010.08499 |