Mini cours

Vincent Guirardel, UPS Toulouse

Limit groups

Abstract

The limit groups have been studied by Sela and Kharlampovich-Miasnikov to understand the elemetary theory of free groups. When the set of marked groups (ie groups together with a distinguished generating set) is endowed with an appropriate topology, the limit groups occur as points in the closure of the set of markings of the free group.

We will give an overview of the properties of limit groups, and show how they can be used to understand the set of solutions of a system of equations in the free group, in particular using the Makanin-Razborov diagram. We will use Sela's approach, using in particular actions on R-trees, and JSJ splittings.