Geometric density for invariant random subgroups of groups acting on CAT(0) spaces

Bruno Duchesne (1) , Yair Glasner (2) , Nir Lazarovich (3) , Jean Lécureux (4)

1 IECL - Institut Élie Cartan de Lorraine
2 Department of Mathematics [Be'er Sheva]
3 TECHNION - Department of Mathematics
4 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We prove that an IRS of a group with a geometrically dense action on a CAT(0) space also acts geometrically densely; assuming the space is either of finite telescopic dimension or locally compact with finite dimensional Tits boundary. This can be thought of as a Borel density theorem for IRSs.

Mots clés: Invariant random subgroups; CAT(0) spaces; Geometric density

Domaines: Théorie des groupes [math.GR]; Géométrie métrique [math.MG]; Mathématiques générales [math.GM]; Géométrie différentielle [math.DG]

Bruno Duchesne, Yair Glasner, Nir Lazarovich, Jean Lécureux. Geometric density for invariant random subgroups of groups acting on CAT(0) spaces. Geometriae Dedicata, 2015, 175 (1), pp.249-256. ⟨hal-01069111⟩