Representation variety of free or surface groups and Reidemeister torsion

Abstract

For G ∈ {GL(n, mathbb{C}), SL(n, mathbb{C})} , we consider G−valued representations of free or surface group with genus > 1. We establish a formula for computing Reidemeister torsion of such representations in terms of Atiyah-Bott-Goldman symplectic form for G. Furthermore, we apply the obtained results to hyperbolic 3-manifolds.