Infinite dimensional non-positively curved symmetric spaces of finite rank

Bruno Duchesne (1, 2)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 Section de mathématiques [Genève]

This paper concerns a study of three families of non-compact type symmetric spaces of infinite dimension. Although they have infinite dimension they have finite rank. More precisely, we show they have finite telescopic dimension. We also show the existence of Furstenberg maps for some group actions on these spaces. Such maps appear as a first step toward superrigidity results.

Domaines: Géométrie différentielle [math.DG]; Théorie des groupes [math.GR]

Bruno Duchesne. Infinite dimensional non-positively curved symmetric spaces of finite rank. International Mathematics Research Notices, 2013, 7, pp.1578-1627. ⟨10.1093/imrn/rns093⟩. ⟨hal-00831405⟩