Complex valued Ray--Singer torsion II

Details Complex valued Ray--Singer torsion II Complex valued Ray--Singer torsion II

2006-10-28

arxiv.org/abs/math/0610875v1

Mathematics

Differential Geometry

35 pages

Scientific paper

In this paper we extend Witten-Helffer-Sj\"ostrand theory from selfadjoint Laplacians based on fiber wise Hermitian structures, to non-selfadjoint Laplacians based on fiber wise non-degenerate symmetric bilinear forms. As an application we verify, up to sign, the conjecture about the comparison of the Milnor-Turaev torsion with the complex valued analytic torsion, for odd dimensional manifolds. This is done along the lines of Burghelea, Friedlander and Kappeler's proof of the Cheeger-M\"uller theorem.

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