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Refined analytic torsion as an element of the determinant line


Braverman, M; Kappeler, T (2007). Refined analytic torsion as an element of the determinant line. Geometry & Topology, 11:139-213.

Abstract

We construct a canonical element, called the refined analytic torsion, of the determinant line of the cohomology of a closed oriented odd-dimensional manifold M with coefficients in a flat complex vector bundle E. We compute the Ray–Singer norm of the refined analytic torsion. In particular, if there exists a flat Hermitian metric on E, we show that this norm is equal to 1. We prove a duality theorem, establishing a relationship between the refined analytic torsions corresponding to a flat connection and its dual.

Abstract

We construct a canonical element, called the refined analytic torsion, of the determinant line of the cohomology of a closed oriented odd-dimensional manifold M with coefficients in a flat complex vector bundle E. We compute the Ray–Singer norm of the refined analytic torsion. In particular, if there exists a flat Hermitian metric on E, we show that this norm is equal to 1. We prove a duality theorem, establishing a relationship between the refined analytic torsions corresponding to a flat connection and its dual.

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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:07 Dec 2009 12:17
Last Modified:05 Apr 2016 13:23
Publisher:Mathematical Sciences Publishers
ISSN:1364-0380
Publisher DOI:https://doi.org/10.2140/gt.2007.11.139
Related URLs:http://arxiv.org/abs/math/0510532

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