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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Refined analytic torsion as an element of the determinant line

Maxim Braverman and Thomas Kappeler

Geometry & Topology 11 (2007) 139–213

arXiv: math.GT/0510532

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.

Keywords
determinant line, Ray–Singer, eta-invariant, analytic torsion
Mathematical Subject Classification 2000
Primary: 58J52
Secondary: 58J28, 57R20
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Publication
Received: 29 March 2006
Accepted: 21 November 2006
Published: 16 March 2007
Proposed: Peter Teichner
Seconded: Wolfgang Lueck, Leonid Polterovich
Authors
Maxim Braverman
Department of Mathematics
Northeastern University
Boston MA 02115
USA
Thomas Kappeler
Institut fur Mathematik
Universitat Zürich
Winterthurerstrasse 190
CH-8057 Zürich
Switzerland