Twisted Alexander polynomials of 2-bridge knots associated to metacyclic representations
| dc.creator | Hirasawa, Mikami | |
| dc.creator | Murasugi, Kunio | |
| dc.date | 2009-03-01 | |
| dc.date.accessioned | 2026-07-07T12:48:01Z | |
| dc.date.available | 2026-07-07T12:48:01Z | |
| dc.description | Let p be an odd prime and D_p a dihedral group of order 2p. Let ρ: G(K) --> D_p --> GL(p,Z) be a non-abelian representation of the knot group G(K) of a knot K in 3-sphere. Let Δ_{ρ,K} (t) be the twisted Alexander polynomial of K associated to ρ. Let H(p) is the set of 2-bridge knots K, such that G(K) is mapped onto a non-trivial free product Z/2 * Z/p. Then we prove that for any 2-bridge knot K in H(p), Δ_{ρ,K}(t) is of the form Δ_{K}(t)/(1-t) f(t) f(-t) for some integer polynomial f(t), where Δ_K (t) is the Alexander polynomial of K. Further, it is proved that f(t) \equiv {Δ_K (t)/(1+t)}^n (mod p). Later we discuss the twisted Alexander polynomial associated to the general metacyclic representation. | |
| dc.identifier | https://arxiv.org/abs/0903.0147 | |
| dc.identifier | http://arxiv.org/abs/0903.0147 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221913 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25,57M27 | |
| dc.title | Twisted Alexander polynomials of 2-bridge knots associated to metacyclic representations | |
| dc.type | text |