Analytic and Reidemeister torsion for representations in finite type Hilbert modules

Burghelea, D.; Friedlander, L.; Kappeler, T.; McDonald, P.

Analytic and Reidemeister torsion for representations in finite type Hilbert modules

Authors

Description

For a closed Riemannian manifold we extend the definition of analytic and Reidemeister torsion associated to an orthogonal representation of fundamental group on a Hilbert module of finite type over a finite von Neumann algebra. If the representation 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 Reidemeister torsions are equal.
78 pages, AMSTeX