Displaying similar documents to “Quillen metrics and higher analytic torsion forms.”

Reidemeister Torsion and Analytic Torsion of Discs

T. de Melo, L. Hartmann, M. Spreafico (2009)

Bollettino dell'Unione Matematica Italiana

Similarity:

We study the Reidemeister torsion and the analytic torsion of the m-dimensional disc in the Euclidean m-dimensional space, using the base for the homology defined by Ray and Singer in [10]. We prove that the Reidemeister torsion coincides with the square root of the volume of the disc. We study the additional terms arising in the analytic torsion due to the boundary, using generalizations of the Cheeger-Müller theorem. We use a formula proved by Brüning and Ma [1], that predicts a new...

Comparison of the refined analytic and the Burghelea-Haller torsions

Maxim Braverman, Thomas Kappeler (2007)

Annales de l’institut Fourier

Similarity:

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 ± 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...