Analytic and Reidemeister torsion for representations in finite type Hilbert modules

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

1995-02-03

arxiv.org/abs/dg-ga/9502001v1

Mathematics

Differential Geometry

78 pages, AMSTeX

Scientific paper

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-M\"uller 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.

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