Analytic torsion of complete hyperbolic manifolds of finite volume

TL;DR

This paper defines the analytic torsion for finite volume hyperbolic manifolds and investigates its asymptotic behavior for sequences of representations, contributing to geometric analysis and spectral theory.

Contribution

It introduces the concept of analytic torsion for complete hyperbolic manifolds of finite volume and analyzes its asymptotics for specific representation sequences.

Findings

Analytic torsion is well-defined for these manifolds.

Asymptotic behavior of torsion is characterized for certain representations.

Results extend understanding of spectral invariants in hyperbolic geometry.

Abstract

In this paper we define the analytic torsion for a complete oriented hyperbolic manifold of finite volume. It depends on a representation of the fundamental group. For manifolds of odd dimension, we study the asymptotic behavior of the analytic torsion with respect to certain sequences of representations obtained by restriction of irreducible representations of the group of isometries of the hyperbolic space to the fundamental group.