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 SL2()–representations of a knot group. A bifurcation point in the SL2()–character variety of a knot group is a character which is given by both an abelian SL2()–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
Mathematical Subject Classification 2000
Primary: 57Q10
Secondary: 57M05
References
Publication
Received: 1 February 2007
Revised: 28 July 2007
Accepted: 22 August 2007
Published: 14 November 2007
Authors
Yoshikazu Yamaguchi
Graduate School of Mathematical Sciences
University of Tokyo
3-8-1 Komaba Meguro
Tokyo 153-8914
Japan