** "Geometry and Analysis on Groups" Research Seminar **

**Time:** 2014.11.11, 15:00--17:00

**Location:** Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock

**Title:** "On a property of geometric actions of groups"

**Speaker:** Jean Raimbault (Université Paul Sabatier, Toulouse III)

**Abstract:**
The notion of a diffuse group was introduced by B. Bowditch as a geometric analogue of the unique products property. Its definition can be extended to group actions, and Bowditch established that free, semisimple actions of finitely generated groups on hyperbolic spaces are 'virtually' diffuse (i.e. there is a finite-index subgroup which acts diffusely). In the first part of this talk I will introduce the definitions and examples from Bowditch's paper, and in the second part I will present results from a recent work (joint with S.Kionke) which prove virtual diffuseness in many more settings, e.g. :
- Kleinian groups (in dimension 3) containg parabolics
- Three--manifold groups

I will also try to discuss new examples of non-diffuse groups (mainly crystallographic groups).