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Relative torsion


Burghelea, D; Friedlander, L; Kappeler, T (2001). Relative torsion. Communications in Contemporary Mathematics, 3(1):15-85.

Abstract

This paper achieves, among other things, the following:
• It frees the main result of [9] from the hypothesis of determinant class and extends this result from unitary to arbitrary representations.
• It extends (and at the same times provides a new proof of) the main result of Bismut and Zhang [3] from finite dimensional representations of Γ to representations on an A-Hilbert module of finite type (A a finite von Neumann algebra). The result of [3] corresponds to A = C .
• It provides interesting real valued functions on the space of representations of the fundamental group Γ of a closed manifold M. These functions might be a useful source of topological and geometric invariants of M.
These objectives are achieved with the help of the relative torsion ℛ, first introduced by Carey, Mathai and Mishchenko [12] in special cases. The main result of this paper calculates explicitly this relative torsion (cf. Theorem 1.1).

This paper achieves, among other things, the following:
• It frees the main result of [9] from the hypothesis of determinant class and extends this result from unitary to arbitrary representations.
• It extends (and at the same times provides a new proof of) the main result of Bismut and Zhang [3] from finite dimensional representations of Γ to representations on an A-Hilbert module of finite type (A a finite von Neumann algebra). The result of [3] corresponds to A = C .
• It provides interesting real valued functions on the space of representations of the fundamental group Γ of a closed manifold M. These functions might be a useful source of topological and geometric invariants of M.
These objectives are achieved with the help of the relative torsion ℛ, first introduced by Carey, Mathai and Mishchenko [12] in special cases. The main result of this paper calculates explicitly this relative torsion (cf. Theorem 1.1).

Citations

9 citations in Web of Science®
6 citations in Scopus®
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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
Uncontrolled Keywords:strong Fredholm type operators; ξ-regularized complex; Witten deformation; Reidemeister torsion; analytic torsion
Language:English
Date:2001
Deposited On:18 Feb 2010 13:08
Last Modified:05 Apr 2016 13:25
Publisher:World Scientific Publishing
ISSN:0219-1997
Additional Information:Electronic version of an article published as [Commun. Contemp. Math. 3 (2001), no. 1, 15–85] http://dx.doi.org/10.1142/S0219199701000287 © copyright World Scientific Publishing Company http://www.worldscinet.com/ccm/ccm.shtml
Publisher DOI:https://doi.org/10.1142/S0219199701000287
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1820014
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0994.58018
Permanent URL: https://doi.org/10.5167/uzh-22004

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