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Comparison of the refined analytic and the Burghelea-Haller torsions

Maxim Braverman; Thomas Kappeler — 2007

Annales de l’institut Fourier

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 $\pm τ$ . 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...

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