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Comparison of the refined analytic and the Burghelea-Haller torsions

Maxim Braverman·Thomas Kappeler
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Abstract

The refined analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold canonically defines a quadratic form $τ$ on the determinant line of the cohomology. Both $τ$ and the Burghelea-Haller torsion are refinements of the Ray-Singer torsion. We show that whenever the Burghelea-Haller torsion is defined it is equal to $\pmτ$. As an application we obtain new results about the Burghelea-Haller torsion. In particular, we prove a weak version of the Burghelea-Haller conjecture relating their torsion with the square of the Farber-Turaev combinatorial torsion.

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Maxim Braverman, Thomas Kappeler. 2007-06-28. Comparison of the refined analytic and the Burghelea-Haller torsions. https://arxiv.org/abs/math/0606398

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