La torsion analytique raffinée, associée à un fibré vectoriel plat sur une variété fermée et orientée de dimension impaire, définit d’une manière canonique une forme quadratique sur le déterminant de la cohomologie. La torsion introduite par Burghelea et Haller et la forme quadratique sont des concepts raffinés de la torsion analytique de Ray-Singer. On démontre que dans le cas où la torsion de Burghelea-Haller est définie, elle est identique à . Comme application, on obtient des résultats nouveaux pour la torsion de Burghelea-Haller. En particulier, on démontre une version faible de la conjecture de Burghelea-Haller concernant leur torsion et le carré de la torsion combinatoire de Farber-Turaev.
The refined analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold canonically defines a quadratic form on the determinant line of the cohomology. Both 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 . 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.
@article{AIF_2007__57_7_2361_0,
author = {Braverman, Maxim and Kappeler, Thomas},
title = {Comparison of the refined analytic and the Burghelea-Haller torsions},
journal = {Annales de l'Institut Fourier},
volume = {57},
year = {2007},
pages = {2361-2387},
doi = {10.5802/aif.2336},
zbl = {1147.58033},
mrnumber = {2394545},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_2007__57_7_2361_0}
}
Braverman, Maxim; Kappeler, Thomas. Comparison of the refined analytic and the Burghelea-Haller torsions. Annales de l'Institut Fourier, Tome 57 (2007) pp. 2361-2387. doi : 10.5802/aif.2336. http://gdmltest.u-ga.fr/item/AIF_2007__57_7_2361_0/
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