Analytic torsion of generic rank two distributions in dimension five

Abstract

We propose an analytic torsion for the Rumin complex associated with generic rank two distributions on closed 5-manifolds. This torsion behaves as expected with respect to Poincare duality and finite coverings. We establish anomaly formulas, expressing the dependence on the sub-Riemannian metric and the 2-plane bundle in terms of integrals over local quantities. For certain nilmanifolds we are able to show that this torsion coincides with the Ray-Singer analytic torsion, up to a constant.

60 pages

References in corpus (5)

• Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds - Characterization and Killing-Field Decomposition
• The twistor spinors of generic 2- and 3-distributions
• On Nurowski's conformal structure associated to a generic rank two distribution in dimension five
• On automorphism groups of some types of generic distributions
• Sub-Riemannian limit of the differential form heat kernels of contact manifolds

Cited by in corpus (3)

• Comparing three possible hypoelliptic Laplacians on the 5-dimensional Cartan group via div-curl type estimates
• Analytic torsion of nilmanifolds with (2,3,5) distributions
• Regularized determinants of the Rumin complex in irreducible unitary representations of the (2,3,5) nilpotent Lie group