Representation variety of free or surface groups and Reidemeister torsion

Authors: FATİH HEZENCİ, YAŞAR SÖZEN

Abstract: For $G \in \left\{ \mathrm{GL}(n,\mathbb{C}) , \mathrm{SL}(n,\mathbb{C})\right\} ,$ 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.

Keywords: Reidemeister torsion, representation varieties, Atiyah-Bott-Goldman symplectic form, symplectic chain complex, hyperbolic 3-manifolds

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