Nous définissons et étudions la torsion analytique du complexe de contact sur les variétés de contact. Nous montrons qu’elle coïncide avec la torsion de Ray–Singer sur les variétés CR de Seifert munies d’une représentation unitaire. Nous la calculons dans ces cas et l’exprimons à l’aide de propriétés dynamiques du flot de Reeb. En fait, notre fonction spectrale de torsion analytique coïncide avec une fonction zêta dynamique naturelle. Ces formules de trace « à la Selberg » persistent ici pour des métriques de courbure non constante sur la base.
We propose a definition for analytic torsion of the contact complex on contact manifolds. We show it coincides with Ray–Singer torsion on any
Keywords: analytic torsion, contact complex, CR Seifert manifold, trace formula
Mot clés : torsion analytique, complexe de contact, variété CR de Seifert, formule de trace
@article{AIF_2012__62_2_727_0, author = {Rumin, Michel and Seshadri, Neil}, title = {Analytic torsions on contact manifolds}, journal = {Annales de l'Institut Fourier}, pages = {727--782}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {62}, number = {2}, year = {2012}, doi = {10.5802/aif.2693}, zbl = {1264.58027}, mrnumber = {2985515}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2693/} }
TY - JOUR AU - Rumin, Michel AU - Seshadri, Neil TI - Analytic torsions on contact manifolds JO - Annales de l'Institut Fourier PY - 2012 SP - 727 EP - 782 VL - 62 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2693/ DO - 10.5802/aif.2693 LA - en ID - AIF_2012__62_2_727_0 ER -
%0 Journal Article %A Rumin, Michel %A Seshadri, Neil %T Analytic torsions on contact manifolds %J Annales de l'Institut Fourier %D 2012 %P 727-782 %V 62 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2693/ %R 10.5802/aif.2693 %G en %F AIF_2012__62_2_727_0
Rumin, Michel; Seshadri, Neil. Analytic torsions on contact manifolds. Annales de l'Institut Fourier, Tome 62 (2012) no. 2, pp. 727-782. doi : 10.5802/aif.2693. http://www.numdam.org/articles/10.5802/aif.2693/
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