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

2005/12/13 by Yoshikazu Yamaguchi, Yamaguchi, Yoshikazu
Mathematics · Medicine · #57M05 #57M25 #57M27 #57Q10 #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57M05 #msc:57M25 #msc:57M27 #msc:57Q10

paper · pdf · doi:10.48550/arxiv.math/0512267

to appear in Ann. Institut Fourier

openalex publication_date 2005/12/13 · arxiv created 2007/07/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Non-abelian Reidemeister torsion for twist knots
• Non abelian Reidemeister torsion and volume form on the SU(2)-representation space of knot groups
• Non abelian twisted Reidemeister torsion for fibered knots
• Higher even dimensional Reidemeister torsion for torus knot exteriors
• The twisted Reidemeister torsion of an iterated torus knot