Twisted Alexander polynomials of hyperbolic links

Abstract

In this paper we apply the twisted Alexander polynomial to study the fibering and genus detecting problems for oriented links. In particular we generalize a conjecture of Dunfield, Friedl and Jackson on the torsion polynomial of hyperbolic knots to hyperbolic links, and confirm it for an infinite family of hyperbolic 2-bridge links. Moreover we consider a similar problem for parabolic representations of 2-bridge link groups.

19 pages, 3 figures. Title changed. Section 3 (Finiteness theorems for alternating links) of the old version is removed, since there is a gap in the proof of Theorem 3.3. A new section on parabolic representations (Section 5) is added in the new version