Seminar

The curve complex (or graph if we are only interested in its 1-skeleton) is a wonderful tool for proving theorems about mapping class groups of surfaces. Some of these theorems are also true, or we at least hope are true, for automorphism groups of free groups. Much recent progress has focused on understanding analogous objects to the curve graph in the free group setting. We will give a survey of some recent results. We talk about one reason for the existence of multiple graphs in this setting: there is more than one way of describing what a ‘simple closed curve in a surface’ should be in a free group.