Limit values of the non-acyclic Reidemeister torsion for knots

Abstract

We consider the Reidemeister torsion associated with ${SL}_2\left(ℂ\right)$–representations of a knot group. A bifurcation point in the ${SL}_2\left(ℂ\right)$–character variety of a knot group is a character which is given by both an abelian ${SL}_2\left(ℂ\right)$–representation and a nonabelian 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.