Torsion function on character varieties

Abstract

In this paper we define the Reidemeister torsion as a rational function on the geometric components of the character variety of a one-cusped hyperbolic manifold M. We study its poles and zeros, and we deduce sufficient conditions on the manifold M for this function being non-constant.

26 pages, 5 figures, comments welcome. v2: Many corrections and improvements, Section 5.2 and Lemma 2.18 rewritten. This version is accepted for publication in Osaka Journal of Mathematics

References in corpus (1)

• Representations of knot groups into ${\mathrm{SL}}_n(\mathbf{C})$ and twisted Alexander polynomials