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Twisted Alexander polynomials of genus one two-bridge knots

Research paper by Anh T. Tran

Indexed on: 16 Jun '15Published on: 16 Jun '15Published in: Mathematics - Geometric Topology



Abstract

Morifuji computed the twisted Alexander polynomial of twist knots for nonabelian representations. In this paper we compute the twisted Alexander polynomial and the Reidemeister torsion of genus one two-bridge knots, a class of knots which includes twist knots. As an application, we give a formula for the Reidemeister torsion of the 3-manifold obtained by a Dehn surgery on a genus one two-bridge knot.