Comparison of the refined analytic and the Burghelea-Haller torsions

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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.
To appear in Annales de l'institut Fourier. Compared to the first version many statements are refined and improved

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Differential Geometry, Mathematical Physics, 58J52; 58J28, 57R20

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http://salesiana.dossiersoluciones.com/handle/123456789/132574

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0606398
 http://arxiv.org/abs/math/0606398

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arXiv