Analytic torsions on contact manifolds

TL;DR

This paper introduces a new definition of analytic torsion for contact manifolds, demonstrates its equivalence to Ray-Singer torsion in specific cases, and links it to dynamical properties of Reeb flows on CR Seifert manifolds.

Contribution

It defines analytic torsion for the contact complex and connects it to dynamical systems and spectral theory on CR Seifert manifolds.

Findings

Analytic torsion coincides with Ray-Singer torsion on 3D CR Seifert manifolds.

Computed the torsion explicitly in certain cases.

Linked spectral torsion to dynamical properties via trace formulae.

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.