#### Volume 7, issue 3 (2007)

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Limit values of the non-acyclic Reidemeister torsion for knots

### Yoshikazu Yamaguchi

Algebraic & Geometric Topology 7 (2007) 1485–1507
 arXiv: math.GT/0512277
##### 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.

##### Keywords
Reidemeister torsion, twisted Alexander invariant, knots, character varieties
Primary: 57Q10
Secondary: 57M05