Analytic torsions on contact manifolds

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-type trace formulae.

40 pages

References in corpus (2)

• Finite energy Seiberg-Witten moduli spaces on 4-manifolds bounding Seifert fibrations
• Approximately Einstein ACH metrics, volume renormalization, and an invariant for contact manifolds

Cited by in corpus (9)

• Graded hypoellipticity of BGG sequences
• The heat asymptotics on filtered manifolds
• Pushing down the Rumin complex to conformally symplectic quotients
• Analytic torsion of generic rank two distributions in dimension five
• Analytic torsions associated with the Rumin complex on contact spheres
• Dynamical torsion for contact Anosov flows
• Comparing three possible hypoelliptic Laplacians on the 5-dimensional Cartan group via div-curl type estimates
• Regularized determinants of the Rumin complex in irreducible unitary representations of the (2,3,5) nilpotent Lie group
• Analytic torsion of nilmanifolds with (2,3,5) distributions