A new proof of a Bismut-Zhang formula for some class of representations

Maxim Braverman; Boris Vertman

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arXiv · 1304.5365

A new proof of a Bismut-Zhang formula for some class of representations

Maxim Braverman·Boris Vertman

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Abstract

Bismut and Zhang computed the ratio of the Ray-Singer and the combinatorial torsions corresponding to non-unitary representations of the fundamental group. In this note we show that for representations which belong to a connected component containing a unitary representation the Bismut-Zhang formula follows rather easily from the Cheeger-Mueller theorem, i.e. from the equality of the two torsions on the set of unitary representations. The proof uses the fact that the refined analytic torsion is a holomorphic function on the space of representations.

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Maxim Braverman, Boris Vertman. 2013-04-19. A new proof of a Bismut-Zhang formula for some class of representations. https://arxiv.org/abs/1304.5365

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