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.

arXiv comment60 pages

References in corpus (24)

• Differential equations and conformal structures
• Complex valued Ray-Singer torsion
• Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds - Characterization and Killing-Field Decomposition
• On the tangent groupoid of a filtered manifold
• The twistor spinors of generic 2- and 3-distributions
• Twistor space for rolling bodies
• Subcomplexes in Curved BGG-Sequences
• Complex valued Ray--Singer torsion II
• Torsion and fibrations
• On Nurowski's conformal structure associated to a generic rank two distribution in dimension five
• Graded hypoellipticity of BGG sequences
• Refined Analytic Torsion as an Element of the Determinant Line
• Tangent Maps and Tangent Groupoid for Carnot Manifolds
• The heat asymptotics on filtered manifolds
• Analytic torsions on contact manifolds
• Nearly Kähler Geometry and $(2,3,5)$-Distributions via Projective Holonomy
• On automorphism groups of some types of generic distributions
• On the deformation groupoid of the inhomogeneous pseudo-differential Calculus
• The Geometry of Almost Einstein (2,3,5) Distributions
• New relations between $G_2$-geometries in dimensions 5 and 7
• On 5-manifolds admitting rank two distributions of Cartan type
• The Engel-Lutz twist and overtwisted Engel structures
• Loose Engel structures
• Sub-Riemannian limit of the differential form heat kernels of contact manifolds

Cited by in corpus (4)

• Graded hypoellipticity of BGG sequences
• 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