# Analytic and Reidemeister torsion for representations in finite type Hilbert modules

Burghelea, D; Friedlander, L; Kappeler, T; McDonald, P (1996). Analytic and Reidemeister torsion for representations in finite type Hilbert modules. Geometric and Functional Analysis, 6(5):751-859.

## Abstract

For a closed Riemannian manifold (M, g) we extend the definition of analytic and Reidemeister torsion associated to a unitary representation of π₁(M) on a finite dimensional vector space to a representation on a A-Hilbert module W of finite type where A is a finite von Neumann algebra. If (M,W) is of determinant class we prove, generalizing the Cheeger-Müller theorem, that the analytic and Reidemeister torsion are equal. In particular, this proves the conjecture that for closed Riemannian manifolds with positive Novikov-Shubin invariants, the L₂-analytic and L₂-Reidemeister torsions are equal.

For a closed Riemannian manifold (M, g) we extend the definition of analytic and Reidemeister torsion associated to a unitary representation of π₁(M) on a finite dimensional vector space to a representation on a A-Hilbert module W of finite type where A is a finite von Neumann algebra. If (M,W) is of determinant class we prove, generalizing the Cheeger-Müller theorem, that the analytic and Reidemeister torsion are equal. In particular, this proves the conjecture that for closed Riemannian manifolds with positive Novikov-Shubin invariants, the L₂-analytic and L₂-Reidemeister torsions are equal.

## Citations

31 citations in Web of Science®
27 citations in Scopus®