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Analytic and Reidemeister torsion for representations in finite type Hilbert modules


Burghelea, D; Friedlander, L; Kappeler, T; McDonald, P (1996). Analytic and Reidemeister torsion for representations in finite type Hilbert modules. Geometric and Functional Analysis, 6(5):751-859.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1996
Deposited On:29 Nov 2010 16:28
Last Modified:06 Dec 2017 21:05
Publisher:Birkhäuser
ISSN:1016-443X
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/BF02246786
Related URLs:http://www.digizeitschriften.de/dms/img/?PPN=PPN359089402_0006&DMDID=dmdlog38
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0874.57025

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