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Ray-Singer type theorem for the refined analytic torsion


Braverman, M; Kappeler, T (2007). Ray-Singer type theorem for the refined analytic torsion. Journal of Functional Analysis, 243(1):232-256.

Abstract

We show that the refined analytic torsion is a holomorphic section of the determinant line bundle over the space of complex representations of the fundamental group of a closed oriented odd-dimensional manifold. Further, we calculate the ratio of the refined analytic torsion and the Farber–Turaev combinatorial torsion. As an application, we establish a formula relating the eta-invariant and the phase of the Farber–Turaev torsion, which extends a theorem of Farber and earlier results of ours. This formula allows to study the spectral flow using methods of combinatorial topology.

Abstract

We show that the refined analytic torsion is a holomorphic section of the determinant line bundle over the space of complex representations of the fundamental group of a closed oriented odd-dimensional manifold. Further, we calculate the ratio of the refined analytic torsion and the Farber–Turaev combinatorial torsion. As an application, we establish a formula relating the eta-invariant and the phase of the Farber–Turaev torsion, which extends a theorem of Farber and earlier results of ours. This formula allows to study the spectral flow using methods of combinatorial topology.

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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:09 Apr 2009 20:10
Last Modified:18 Feb 2018 12:48
Publisher:Elsevier
ISSN:0022-1236
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1016/j.jfa.2006.10.008
Related URLs:http://arxiv.org/abs/math/0603638

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Download PDF  'Ray-Singer type theorem for the refined analytic torsion'.
Preview
Content: Accepted Version
Filetype: PDF (Accepted manuscript, Version 1)
Size: 330kB