Analytic and Reidemeister torsion for representations in finite type Hilbert modules
- Cite this article as:
- Burghelea, D., Kappeler, T., McDonald, P. et al. Geometric and Functional Analysis (1996) 6: 751. doi:10.1007/BF02246786
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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.