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

**Time:** 2015.11.24, 15:00--17:00

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

**Title:** "The Tits alternative for non-spherical triangles of groups."

**Speaker:** Johannes Cuno (Technische Universität Graz)

**Abstract:**
Triangles of groups have been introduced by Gersten and Stallings. They are, roughly speaking, a generalization of the amalgamated free product of two groups. It has been shown by Howie and Kopteva that the colimit of a hyperbolic triangle of groups contains a non-abelian free subgroup. We use billiards on triangular tables to give two natural conditions, each of which ensures that the colimit of a non-spherical triangle of groups either contains a non-abelian free subgroup or is virtually solvable. (This is joint work with Jörg Lehnert.)