Reidemeister torsion, hyperbolic three-manifolds, and character varieties

Abstract

This is a survey on Reidemeister torsion for hyperbolic three-manifolds of finite volume. Torsions are viewed as topological invariants and also as functions on the variety of representations in ${\mathrm{SL}}_2(\mathbb{C})$. In both cases, the torsions may also be computed after composing with finite dimensional representations of ${\mathrm{SL}}_2(\mathbb{C})$. In addition the paper deals with the torsion of the adjoint representation as a function on the variety of ${\mathrm{PSL}}_{n+1}(\mathbb{C})$-characters, using that the first cohomology group with coefficients twisted by the adjoint is the tangent space to the variety of characters.

References in corpus (6)

• SL(2,C) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial
• Geometry of the SL(3,C)-character variety of torus knots
• Reidemeister torsion of a 3-manifold obtained by a Dehn-surgery along the figure-eight knot
• The SL(3,C)-character variety of the figure eight knot
• The asymptotic behavior of the Reidemeister torsion for Seifert manifolds and PSL(2;R)-representations of Fuchsian groups
• Twisted Alexander polynomials, character varieties and Reidemeister torsion of double branched covers

Cited by in corpus (6)

• On the structure of tidally-disrupted stellar debris streams
• All-Order Volume Conjecture for Closed 3-Manifolds from Complex Chern-Simons Theory
• Some numerical computations on Reidemeister torsion for homology 3-spheres obtained by Dehn surgeries along the figure-eight knot
• The asymptotics of the higher dimensional Reidemeister torsion for exceptional surgeries along twist knots
• A polynomial defined by the $SL(2;\mathbb{C})$-Reidemeister torsion for a homology 3-sphere obtained by Dehn-surgery along a torus knot
• Hyperbolic Volume and Twisted Alexander invariants of Knots and Links