Analytic torsions on contact manifolds

Michel Rumin[1]; Neil Seshadri[2]

  • [1] Laboratoire de Mathématiques d’Orsay CNRS et Université Paris Sud 91405 Orsay Cedex France
  • [2] Graduate School of Mathematical Sciences The University of Tokyo 3–8– 1 Komaba, Meguro, Tokyo 150-0044 Japan

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 2, page 727-782
  • ISSN: 0373-0956

Abstract

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We propose a definition for analytic torsion of the contact complex on contact manifolds. We show it coincides with Ray–Singer torsion on any 3 -dimensional CR Seifert manifold equipped with a unitary representation. In this particular case we compute it and relate it to dynamical properties of the Reeb flow. In fact the whole spectral torsion function we consider may be interpreted on CR Seifert manifolds as a purely dynamical function through Selberg-like trace formulae, that hold also in variable curvature.

How to cite

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Rumin, Michel, and Seshadri, Neil. "Analytic torsions on contact manifolds." Annales de l’institut Fourier 62.2 (2012): 727-782. <http://eudml.org/doc/251147>.

@article{Rumin2012,
abstract = {We propose a definition for analytic torsion of the contact complex on contact manifolds. We show it coincides with Ray–Singer torsion on any $3$-dimensional CR Seifert manifold equipped with a unitary representation. In this particular case we compute it and relate it to dynamical properties of the Reeb flow. In fact the whole spectral torsion function we consider may be interpreted on CR Seifert manifolds as a purely dynamical function through Selberg-like trace formulae, that hold also in variable curvature.},
affiliation = {Laboratoire de Mathématiques d’Orsay CNRS et Université Paris Sud 91405 Orsay Cedex France; Graduate School of Mathematical Sciences The University of Tokyo 3–8– 1 Komaba, Meguro, Tokyo 150-0044 Japan},
author = {Rumin, Michel, Seshadri, Neil},
journal = {Annales de l’institut Fourier},
keywords = {analytic torsion; contact complex; CR Seifert manifold; trace formula},
language = {eng},
number = {2},
pages = {727-782},
publisher = {Association des Annales de l’institut Fourier},
title = {Analytic torsions on contact manifolds},
url = {http://eudml.org/doc/251147},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Rumin, Michel
AU - Seshadri, Neil
TI - Analytic torsions on contact manifolds
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 2
SP - 727
EP - 782
AB - We propose a definition for analytic torsion of the contact complex on contact manifolds. We show it coincides with Ray–Singer torsion on any $3$-dimensional CR Seifert manifold equipped with a unitary representation. In this particular case we compute it and relate it to dynamical properties of the Reeb flow. In fact the whole spectral torsion function we consider may be interpreted on CR Seifert manifolds as a purely dynamical function through Selberg-like trace formulae, that hold also in variable curvature.
LA - eng
KW - analytic torsion; contact complex; CR Seifert manifold; trace formula
UR - http://eudml.org/doc/251147
ER -

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