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Comparison of the refined analytic and the Burghelea-Haller torsions


Braverman, M; Kappeler, T (2007). Comparison of the refined analytic and the Burghelea-Haller torsions. Annales de l'Institut Fourier, 57(7):2361-2387.

Abstract

The refined analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold canonically defines a quadratic form $\tau $ on the determinant line of the cohomology. Both $\tau $ and the Burghelea-Haller torsion are refinements of the Ray-Singer torsion. We show that whenever the Burghelea-Haller torsion is defined it is equal to $\pm \tau $. As an application we obtain new results about the Burghelea-Haller torsion. In particular, we prove a weak version of the Burghelea-Haller conjecture relating their torsion with the square of the Farber-Turaev combinatorial torsion.

Abstract

The refined analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold canonically defines a quadratic form $\tau $ on the determinant line of the cohomology. Both $\tau $ and the Burghelea-Haller torsion are refinements of the Ray-Singer torsion. We show that whenever the Burghelea-Haller torsion is defined it is equal to $\pm \tau $. As an application we obtain new results about the Burghelea-Haller torsion. In particular, we prove a weak version of the Burghelea-Haller conjecture relating their torsion with the square of the Farber-Turaev combinatorial torsion.

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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:2007
Deposited On:10 Apr 2009 09:56
Last Modified:05 Apr 2016 13:07
Publisher:Association des Annales de l'Institut Fourier
ISSN:0373-0956
Official URL:http://aif.cedram.org/cgi-bin/item?id=AIF_2007__57_7_2361_0
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2394545

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