Analytic torsion of nilmanifolds with (2,3,5) distributions

Abstract

We consider generic rank two distributions on 5-dimensional nilmanifolds, and show that the analytic torsion of their Rumin complex coincides with the Ray-Singer torsion.

arXiv commentv2: minor corrections in the proof of Lemma 9; dropped Remark 4; fixed some typos; no substantial changes; still 32 pages

References in corpus (15)

• Differential equations and conformal structures
• 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
• Twistor space for rolling bodies
• Torsion and fibrations
• On Nurowski's conformal structure associated to a generic rank two distribution in dimension five
• Graded hypoellipticity of BGG sequences
• Analytic torsions on contact manifolds
• The heat asymptotics on filtered manifolds
• Nearly Kähler Geometry and $(2,3,5)$-Distributions via Projective Holonomy
• On automorphism groups of some types of generic distributions
• On 5-manifolds admitting rank two distributions of Cartan type
• Analytic torsion of generic rank two distributions in dimension five
• Analytic torsions associated with the Rumin complex on contact spheres
• Comparing three possible hypoelliptic Laplacians on the 5-dimensional Cartan group via div-curl type estimates

Cited by in corpus (1)

• Regularized determinants of the Rumin complex in irreducible unitary representations of the (2,3,5) nilpotent Lie group