Filippa Lo Biundo (University of Leeds) – Carnot groups and the Rumin complex: an overview and construction.

Sub-Riemannian geometry is a generalization of Riemannian geometry and it has been extensively studied in the past 50 years. In this context, Carnot groups play a central role, as they are the sub-Riemannian analogue of Euclidean spaces. They are connected, simply connected Lie groups whose Lie algebra admits a stratification. Thanks to this stratified structure, a particular subcomplex of the de Rham complex, known as the Rumin complex, can be defined on Carnot groups. Introduced by Rumin in the 1990s, it provides a more natural cohomological framework for these groups by selecting a distinguished class of differential forms, often referred to as "intrinsic" forms. In this talk, I will give an overview of Carnot groups and construct the Rumin complex for a special class of Carnot groups: the Heisenberg groups.