Séminaire Géométrie et groupes discrets

# Geometrization of Certain 4-Dimensional Groups

## by Prof. Ludovic Marquis (Université de Rennes I)

Europe/Paris
Amphithéâtre Léon Motchane (IHES)

### Amphithéâtre Léon Motchane

#### IHES

Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Description
We consider discrete groups admitting proper cocompact topological actions by homeomorphisms on $R^4$. We will say that such a group Γ is geometrized if we can build an action of Γ by projective transformations on a properly convex open subset of the real projective 4-space, or a convex cocompact action of Γ on the real hyperbolic 5-space or on its Lorentzian counterpart, the anti-de Sitter 5-space.

Certain uniform lattices of the isometry group of hyperbolic 4-space are geometrizable by the three geometries mentioned above. We will discuss the existence of groups which are not uniform lattices in hyperbolic 4-space, and which yet admit several of these three geometries. If time allows, we will also discuss the corresponding deformation spaces.

This is joint work with Gye-Seon Lee (Heidelberg).
Organized by

Fanny Kassel

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