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.