Asymptotics of analytic torsion for hyperbolic three-manifolds

Abstract

We prove that for certain sequences of hyperbolic three-manifolds with cusps which converge to hyperbolic three-space in a weak (Benjamini-Schramm) sense and certain coefficient systems the regularised analytic torsion approximates the L 2-torsion of the universal cover. We also prove an asymptotic equality between the former and the Reidemeister torsion of the truncated manifolds.