Twisted Alexander vanishing groups of knots
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914563122790400 |
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| author | Ishikawa, Katsumi Morifuji, Takayuki Suzuki, Masaaki |
| author_facet | Ishikawa, Katsumi Morifuji, Takayuki Suzuki, Masaaki |
| contents | In our previous work, we introduced the notion of a twisted Alexander vanishing (TAV) group, defined as a finite group for which the corresponding twisted Alexander polynomial of a knot vanishes. In this paper, we discuss the orders of TAV groups and construct knots whose twisted Alexander polynomials vanish. Moreover, we show that every faithful irreducible representation of a TAV group causes the twisted Alexander polynomial to be zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13291 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Twisted Alexander vanishing groups of knots Ishikawa, Katsumi Morifuji, Takayuki Suzuki, Masaaki Geometric Topology Primary 57K14, Secondary 57K10 In our previous work, we introduced the notion of a twisted Alexander vanishing (TAV) group, defined as a finite group for which the corresponding twisted Alexander polynomial of a knot vanishes. In this paper, we discuss the orders of TAV groups and construct knots whose twisted Alexander polynomials vanish. Moreover, we show that every faithful irreducible representation of a TAV group causes the twisted Alexander polynomial to be zero. |
| title | Twisted Alexander vanishing groups of knots |
| topic | Geometric Topology Primary 57K14, Secondary 57K10 |
| url | https://arxiv.org/abs/2605.13291 |