Complex valued Ray--Singer torsion II

Abstract

In this paper we extend Witten-Helffer-Sjöstrand 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-Müller theorem.

35 pages

References in corpus (2)

• Complex valued Ray-Singer torsion
• Euler structures, the variety of representations and the Milnor-Turaev torsion

Cited by in corpus (9)

• The refined analytic torsion and a well-posed boundary condition for the odd signature operator
• Analytic torsion of generic rank two distributions in dimension five
• Renormalization of determinant lines in Quantum Field Theory
• Anomaly formulas for the complex-valued analytic torsion on compact bordisms
• Burghelea-Haller analytic torsion for twisted de Rham complexes
• Twisted Cappell-Miller holomorphic and analytic torsions
• Cappell-Miller analytic torsion for manifolds with boundary
• A Cheeger-Mueller theorem for symmetric bilinear torsions on manifolds with boundary
• Refined analytic torsion as analytic function on the representation variety and applications