Limit values of the non-acyclic Reidemeister torsion for knots

Yamaguchi, Yoshikazu

doi:10.2140/agt.2007.7.1485

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Limit values of the non-acyclic Reidemeister torsion for knots

Yoshikazu Yamaguchi

Algebraic & Geometric Topology 7 (2007) 1485–1507

DOI: 10.2140/agt.2007.7.1485

arXiv: math.GT/0512277

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 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

Volume 7, issue 3 (2007)