Limit values of the non-acyclic Reidemeister torsion for knots

Yamaguchi, Yoshikazu¹

¹Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro, Tokyo 153-8914, Japan

Algebraic and Geometric Topology, Tome 7 (2007) no. 3, pp. 1485-1507

Résumé

We consider the Reidemeister torsion associated with SL2(ℂ)–representations of a knot group. A bifurcation point in the SL2(ℂ)–character variety of a knot group is a character which is given by both an abelian SL2(ℂ)–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.

Détail

DOI : 10.2140/agt.2007.7.1485

Keywords: Reidemeister torsion, twisted Alexander invariant, knots, character varieties

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