Twisted Alexander polynomials of a knot for group extensions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917490910560256 |
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| author | Ishikawa, Katsumi Morifuji, Takayuki Suzuki, Masaaki |
| author_facet | Ishikawa, Katsumi Morifuji, Takayuki Suzuki, Masaaki |
| contents | In this paper, we discuss twisted Alexander polynomials of a knot for group extensions of a finite group in two directions. Firstly, we provide a mod $p$ formula for the twisted Alexander polynomial of a knot in the $3$-sphere associated with the regular representation of a finite group. Secondly, we consider twisted Alexander polynomials of a knot for a series of central extensions of a finite group. Moreover, we apply these formulas for twisted Alexander polynomials to the study of twisted Alexander vanishing groups and orders for non-fibered knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13288 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Twisted Alexander polynomials of a knot for group extensions Ishikawa, Katsumi Morifuji, Takayuki Suzuki, Masaaki Geometric Topology Primary 57K14, Secondary 57K10, 20F38 In this paper, we discuss twisted Alexander polynomials of a knot for group extensions of a finite group in two directions. Firstly, we provide a mod $p$ formula for the twisted Alexander polynomial of a knot in the $3$-sphere associated with the regular representation of a finite group. Secondly, we consider twisted Alexander polynomials of a knot for a series of central extensions of a finite group. Moreover, we apply these formulas for twisted Alexander polynomials to the study of twisted Alexander vanishing groups and orders for non-fibered knots. |
| title | Twisted Alexander polynomials of a knot for group extensions |
| topic | Geometric Topology Primary 57K14, Secondary 57K10, 20F38 |
| url | https://arxiv.org/abs/2605.13288 |