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Complex valued Ray-Singer torsion

Dan Burghelea·Stefan Haller
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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.

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Dan Burghelea, Stefan Haller. 2006-04-22. Complex valued Ray-Singer torsion. https://doi.org/10.1016/j.jfa.2007.03.027

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