Groups acting on spaces of non-positive curvature

Bruno Duchesne (1)

1 Géométrie

In this survey article, we present some panorama of groups acting on metric spaces of non-positive curvature. We introduce the main examples and their rigidity properties , we show the links between algebraic or analytic properties of the group and geometric properties of the space. Finally, we conclude with a few conjectures in the subject.

Mots clés: and Phrases: Group actions; spaces of non-positive curvature; CAT(0) spaces; rigidity; superrigidity; amenability; Haagerup property; rank rigid-ity conjecture; flat closing conjecture

Domaines: Géométrie différentielle [math.DG]

Bruno Duchesne. Groups acting on spaces of non-positive curvature. 2016. ⟨hal-01288346v1⟩