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.