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A relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion

Research paper by Yoshikazu Yamaguchi

Indexed on: 03 Jul '07Published on: 03 Jul '07Published in: Mathematics - Geometric Topology



Abstract

We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a lambda-regular SU(2) or SL(2, C)-representation of a knot group. Then we give a method to calculate the non-acyclic Reidemeister torsion of a knot exterior. We calculate a new example and investigate the behavior of the non-acyclic Reidemeister torsion associated to a 2-bridge knot and SU(2)-representations of its knot group.