Complex valued Ray-Singer torsion

Abstract

In the spirit of Ray and Singer we define a complex valued analytic torsion using non-selfadjoint Laplacians. We establish an anomaly formula which permits to turn this into a topological invariant. Conjecturally this analytically defined invariant computes the complex valued Reidemeister torsion, including its phase. We establish this conjecture in some non-trivial situations.

Fixed two sign mistakes and added a few more details here and there

References in corpus (4)

• Dynamics, Laplace transform and Spectral geometry
• Euler structures, the variety of representations and the Milnor-Turaev torsion
• Refined Analytic Torsion
• Ray-Singer Type Theorem for the Refined Analytic Torsion

Cited by in corpus (23)

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• A Canonical Quadratic Form on the Determinant Line of a Flat Vector Bundle
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• Rationality of the SL(2,C)-Reidemeister torsion in dimension 3
• Ray-Singer Type Theorem for the Refined Analytic Torsion
• Survey on analytic and topological torsion
• A Cheeger-Mueller theorem for symmetric bilinear torsions
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• Refined analytic torsion as analytic function on the representation variety and applications
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• A Cheeger-Mueller theorem for symmetric bilinear torsions on manifolds with boundary
• Burghelea-Haller analytic torsion for twisted de Rham complexes
• Cappell-Miller analytic torsion for manifolds with boundary
• Reidemeister torsion, complex volume, and Zograf infinite product
• Twisted Cappell-Miller holomorphic and analytic torsions
• Equivariant symmetric bilinear torsions