Twisted Analytic Torsion and Adiabatic Limits

Ryan Mickler

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arXiv · 1311.6788

Twisted Analytic Torsion and Adiabatic Limits

Ryan Mickler

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Abstract

We study an analogue of the analytic torsion for elliptic complexes that are graded by $\mathbb{Z}_2$, orignally constructed by Mathai and Wu. Motivated by topological T-duality, Bouwknegt an Mathai study the complex of forms on an odd-dimensional manifold equipped with with the twisted differential $d_H = d+H$, where $H$ is a closed odd-dimensional form. We show that the Ray-Singer metric on this twisted determinant is equal to the untwisted Ray-Singer metric when the determinant lines are identified using a canonical isomorphism. We also study another analytical invariant of the twisted differential, the derived Euler characteristic $χ'(d_H)$, as defined by Bismut and Zhang.

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Ryan Mickler. 2013-11-26. Twisted Analytic Torsion and Adiabatic Limits. https://arxiv.org/abs/1311.6788

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