Geometric & Functional Analysis GAFA

, Volume 6, Issue 5, pp 751–859

Analytic and Reidemeister torsion for representations in finite type Hilbert modules

  • D. Burghelea
  • T. Kappeler
  • P. McDonald
  • L. Friedlander
Article

DOI: 10.1007/BF02246786

Cite this article as:
Burghelea, D., Kappeler, T., McDonald, P. et al. Geometric and Functional Analysis (1996) 6: 751. doi:10.1007/BF02246786

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, theL2-analytic andL2-Reidemeister torsions are equal.

Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • D. Burghelea
    • 1
  • T. Kappeler
    • 1
  • P. McDonald
    • 1
  • L. Friedlander
    • 2
  1. 1.Department of MathematicsOhio State UniversityColumbusUSA
  2. 2.Department of MathematicsUniversity of ArizonaTucsonUSA