Article

Geometric & Functional Analysis GAFA

, Volume 6, Issue 5, pp 751-859

Analytic and Reidemeister torsion for representations in finite type Hilbert modules

  • D. BurgheleaAffiliated withDepartment of Mathematics, Ohio State University
  • , T. KappelerAffiliated withDepartment of Mathematics, Ohio State University
  • , P. McDonaldAffiliated withDepartment of Mathematics, Ohio State University
  • , L. FriedlanderAffiliated withDepartment of Mathematics, University of Arizona

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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 aA-Hilbert moduleW of finite type whereA 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, theL 2-analytic andL 2-Reidemeister torsions are equal.