A gluing formula for the analytic torsion on hyperbolic manifolds with cusps

Abstract

For an odd-dimensional oriented hyperbolic manifold with cusps and strongly acyclic coefficient systems we define the Reidemeister torsion of the Borel-Serre compactification of the manifold using bases of cohomology classes defined via Eisenstein series by the method of Harder. In the main result of this paper we relate this combinatorial torsion to the regularized analytic torsion. Together with results on the asymptotic behaviour of the regularized analytic torsion, established previously, this should have applications to study the growth of torsion in the cohomology of arithmetic groups. Our main result is established via a gluing formula and here our approach is heavily inspired by a recent paper of Lesch.

References in corpus (3)

• A torsion Jacquet--Langlands correspondence
• Analytic torsion versus Reidemeister torsion on hyperbolic 3-manifolds with cusps
• On the growth of torsion in the cohomology of arithmetic groups

Cited by in corpus (8)

• Analytic torsion and R-torsion of Witt representations on manifolds with cusps
• A Cheeger-Müller theorem for manifolds with wedge singularities
• Cheeger-Mueller Theorem on manifolds with cusps
• Exponential growth of torsion in the cohomology of arithmetic hyperbolic manifolds
• Analytic torsion and Reidemeister torsion of hyperbolic manifolds with cusps
• Resolvent, heat kernel and torsion under degeneration to fibered cusps
• Intersection torsion and analytic torsion of spaces with conical singularities
• Asymptotics of automorphic spectra and the trace formula