Differential complexes adapted to Carnot groups

Abstract:

Carnot groups are nilpotent Lie groups equipped with a horizontal distribution and provide fundamental examples of subRiemannian manifolds. Their anisotropic geometry induces a natural filtration on differential forms, which is not preserved by the de Rham differential. This motivates the search for smaller differential complexes that better reflect the underlying geometry.

In this talk, I will describe the construction of subcomplexes adapted to the filtration of a Carnot group, such as the Rumin complex and spectral complexes, and indicate how they can be used to formulate classical differential-geometric results in the subRiemannian setting.