Refined Analytic Torsion as an Element of the Determinant Line

Details Refined Analytic Torsion as an Element of the Determinant Line Refined Analytic Torsion as an Element of the Determinant Line

2005-10-25

arxiv.org/abs/math/0510532v4

Mathematics

Geometric Topology

A sign in the definition (4.2) is changed (we are grateful to Guangxiang Su for this correction). Some minor misprints are als

Scientific paper

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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