Présidents de session
Around proper actions on homogeneous spaces: Around proper actions on homogeneous spaces I
- Yosuke Morita (Kyushu University)
- Maciej Bocheński (University of Warmia and Mazury in Olsztyn)
Around proper actions on homogeneous spaces: Around proper actions on homogeneous spaces II
- Il n'a pas de président de session pour ce bloc
Around proper actions on homogeneous spaces: Around proper actions on homogeneous spaces III
- Il n'a pas de président de session pour ce bloc
Description
Let G/H be a reductive homogeneous space and Γ be a (torsion-free) discrete subgroup of G. The quotient of G/H by the left Γ-action is always a manifold in the Riemannian setting (i.e. when H is compact), but not always otherwise: the Γ-action on G/H needs to be proper. In the last 40 years or so, the study of proper actions on non-Riemannian homogeneous spaces has been one of the fertile areas in mathematics to which various methods (Lie-theoretic / dynamical / homotopical / ...) were applied and produced partially overlapping but different results. In this mini-course, we plan to discuss the following topics in this area:
- Basics on reductive Lie groups
- Properness criterion in terms of the Cartan projection (Kobayashi, Benoist) and its consequences
- Proper SL(2,R)-actions vs. proper surface group actions (joint work with Maciej Bocheński)
- Necessary conditions for the existence of proper cocompact actions (joint work with Fanny Kassel and Nicolas Tholozan)
If time permits, we will also discuss:
- A conjectural picture of proper cocompact actions (Tholozan's geometric fibration conjecture)
- Relation to Anosov representation theory (Guéritaud-Guichard-Kassel-Wienhard, Kassel-Tholozan, ...)
L'ordre du jour n'a pas encore été rempli.
