Analytic and Reidemeister torsion for representations in finite type Hilbert modules

D. Burghelea, L. Friedlander, T. Kappeler, P. Mcdonald

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)X-859
JournalGeometric and Functional Analysis
Volume6
Issue number5
DOIs
StatePublished - 1996

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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