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A refinement of the Ray-Singer torsion


Braverman, M; Kappeler, T (2005). A refinement of the Ray-Singer torsion. Comptes Rendus Mathematique, 341(8):497-502.

Abstract

We propose a refinement of the Ray–Singer torsion, which can be viewed as an analytic counterpart of the refined combinatorial torsion introduced by Turaev. Given a closed, oriented manifold of odd dimension with fundamental group Γ, the refined torsion is a complex valued, holomorphic function defined for representations of Γ which are close to the space of unitary representations. When the representation is unitary the absolute value of the refined torsion is equal to the Ray–Singer torsion, while its phase is determined by the η-invariant. As an application we extend and improve a result of Farber about the relationship between the absolute torsion of Farber–Turaev and the η-invariant.

Abstract

We propose a refinement of the Ray–Singer torsion, which can be viewed as an analytic counterpart of the refined combinatorial torsion introduced by Turaev. Given a closed, oriented manifold of odd dimension with fundamental group Γ, the refined torsion is a complex valued, holomorphic function defined for representations of Γ which are close to the space of unitary representations. When the representation is unitary the absolute value of the refined torsion is equal to the Ray–Singer torsion, while its phase is determined by the η-invariant. As an application we extend and improve a result of Farber about the relationship between the absolute torsion of Farber–Turaev and the η-invariant.

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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:2005
Deposited On:03 Feb 2010 08:29
Last Modified:05 Apr 2016 13:24
Publisher:Elsevier
ISSN:1631-073X
Publisher DOI:https://doi.org/10.1016/j.crma.2005.09.015

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