Filippa Lo Biundo (University of Leeds) – On the Pansu pullback and differential complexes on Carnot groups

Abstract: In sub-Riemannian geometry, Carnot groups play a role analogous to that of Euclidean spaces in the Riemannian setting. Their special structure allows one to define an intrinsic notion of differentiability, namely Pansu differentiability, which in turn gives rise to the Pansu pullback on differential forms. In this talk, I will discuss how pullback operators interact with the differentials of the de Rham and Rumin complexes, focusing on commutativity properties. If time permits, I will also present a recent result on the commutativity of the Pansu pullback with the differentials arising in the Spectral complexes associated with the de Rham complex.