Evaluations of the twisted Alexander polynomials of 2-bridge knots at $\pm 1$
| dc.creator | Hirasawa, Mikami | |
| dc.creator | Murasugi, Kunio | |
| dc.date | 2008-08-22 | |
| dc.date.accessioned | 2026-07-07T09:57:56Z | |
| dc.date.available | 2026-07-07T09:57:56Z | |
| dc.description | Let $H(p)$ be the set of 2-bridge knots $K$ whose group $G$ is mapped onto a non-trivial free product, $Z/2 * Z/p$, $p$ being odd. Then there is an algebraic integer $s_0$ such that for any $K$ in $H(p)$, $G$ has a parabolic representation $ρ$ into $SL(2, Z[s_0]) \subset SL(2,C)$. Let $Δ(t)$ be the twisted Alexander polynomial associated to $ρ$. Then we prove that for any $K$ in $H(p)$, $Δ(1)=-2s_0^{-1}$ and $Δ(-1)=-2s_0^{-1}μ^2$, where $s_0^{-1}, μ\in Z[s_0]$. The number $μ$ can be recursively evaluated. | |
| dc.identifier | https://arxiv.org/abs/0808.3058 | |
| dc.identifier | http://arxiv.org/abs/0808.3058 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167534 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25 | |
| dc.title | Evaluations of the twisted Alexander polynomials of 2-bridge knots at $\pm 1$ | |
| dc.type | text |