Orateur
Description
A sub-riemannian structure on a manifold $M$ naturally produces a distance $d_{CC}$. The study of the metric space $(M,d_{CC})$ raises 2 natural questions:
- For $x \in M$ is there a metric space that encodes the infinitesimal properties of the structure at $x$ as does the tangent space $(T_xM, g_x)$ in riemannian geometry ?
- If such a space exists what kind of algebraic structure can it be endowed with ?
This problem has been entirely solved by Mohsen in 2021 using the following very elegant and elementary fact: the quotient of any group $G$ by any subgroup $H$ always has a canonical groupoid structure which coincides with the classical quotient group structure as soon as $H$ is normal in $G$. My goal in this talk is to present Mohsen's construction.
