Reidemeister torsion, hyperbolic three-manifolds, and character varieties

2015/11/02 by Porti, Joan · 2 citations
#57M27 #57Q10 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1511.00400

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 SL₂(\mathbb C). In both cases, the torsions may also be computed after composing with finite dimensional representations of SL₂(\mathbb C). In addition the paper deals with the torsion of the adjoint representation as a function on the variety of 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.

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