Twisted Alexander vanishing order of knots
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916704219561984 |
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| author | Ishikawa, Katsumi Morifuji, Takayuki Suzuki, Masaaki |
| author_facet | Ishikawa, Katsumi Morifuji, Takayuki Suzuki, Masaaki |
| contents | Based on a vanishing theorem for non-fibered knots due to Friedl and Vidussi, we define the twisted Alexander vanishing order of a knot to be the order of the smallest finite group such that the corresponding twisted Alexander polynomial is zero. In this paper, we show its basic properties, and provide several explicit values for knots with $10$ or fewer crossings. Moreover, we characterize a finite group admitting the zero-twisted Alexander polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10936 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Twisted Alexander vanishing order of knots Ishikawa, Katsumi Morifuji, Takayuki Suzuki, Masaaki Geometric Topology Primary 57K14, Secondary 57K10 Based on a vanishing theorem for non-fibered knots due to Friedl and Vidussi, we define the twisted Alexander vanishing order of a knot to be the order of the smallest finite group such that the corresponding twisted Alexander polynomial is zero. In this paper, we show its basic properties, and provide several explicit values for knots with $10$ or fewer crossings. Moreover, we characterize a finite group admitting the zero-twisted Alexander polynomial. |
| title | Twisted Alexander vanishing order of knots |
| topic | Geometric Topology Primary 57K14, Secondary 57K10 |
| url | https://arxiv.org/abs/2310.10936 |