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 regularized analytic torsion approximates the $L^2$-torsion of the universal cover under an additional hypothesis. We also prove an asymptotic equality between the former and some Reidemeister torsion of the truncated manifolds.

Final version, 55 pages (minor corrections and details from the previous version). To appear in Commentarii Mathematici Helvetici