Séminaire Géométries ICJ

From homogeneous metric spaces to Lie groups

par Enrico Le Donne

Salle 112 (ICJ)

Salle 112


1er étage bâtiment Braconnier, Université Claude Bernard Lyon 1 - La Doua
We want to better understand the structure of metric spaces that are locally compact, connected and isometrically homogeneous. After the solution of the Hilbert 5th problem, we know that any such a space is quasi-isometric to some Lie groups, which can be chosen to be solvable. Moreover, if in addition such spaces are locally connected and of finite topological dimension, then they are in fact Lie-group quotients. We shall focus on those spaces that are either geodesic metric spaces, or have polynomial growth, or admit self-similarities. Respectively, we shall have Carnot groups, quasi-nilpotent groups, and graded groups. Joint work with M.Cowling, V.Kivioja, A.Ottazzi, and S.Nicolussi Golo.