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Séminaire Géométries ICJ

From homogeneous metric spaces to Lie groups

by Enrico Le Donne

vendredi 17 novembre 2017 de au (Europe/Paris)
at ICJ ( Salle 112 )
1er étage bâtiment Braconnier, Université Claude Bernard Lyon 1 - La Doua
Description
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.