Limit values of the non-acyclic Reidemeister torsion for knots

Abstract

We consider the Reidemeister torsion associated with SL(2, C)-representations of a knot group. A bifurcation point in the SL(2, C)-character variety of a knot group is a character which is given by both an abelian SL(2, C)-representation and a non-abelian one. We show that there exist limits of the non-acyclic Reidemeister torsion at bifurcation points and the limits are expressed by using the derivation of the Alexander polynomial of the knot in this paper.

to appear in Algebraic and Geometric Topology

References in corpus (1)

• A volume form on the SU(2)-representation space of knot groups

Cited by in corpus (5)

• 3d-3d correspondence for mapping tori
• Reidemeister torsion, hyperbolic three-manifolds, and character varieties
• Twisted Alexander invariant and non-abelian Reidemeister torsion for hyperbolic three-dimensional manifolds with cusps
• The asymptotics of the higher dimensional Reidemeister torsion for exceptional surgeries along twist knots
• Non-abelian Reidemeister torsion for twist knots