Felix Klein Lectures

Automorphisms of free groups and outer space

Karen Vogtmann (New York)

Date: May 25 - June 11

Venue: Tuesdays and Thursdays, 14 - 16, Mathematik-Zentrum, Lipschitz Lecture Hall, Endenicher Allee 60, Bonn
 (Due to a public holiday the lecture will be held on the 2nd, not on the 3rd of June. The lectures on the 2nd, 8th and 10th of June will take place in HIM lecture hall, Poppelsdorfer Allee 45) 

Abstract:

Klein's Erlangen program emphasized the fundamental connection between geometric objects and their groups of isometries. The specific geometric objects he studied were homogeneous spaces, and the associated groups were Lie groups. The geometry of these homogeneous spaces was later used by Siegel, Borel, Serre and many others to understand properties of lattices subgroups of these Lie groups. A similar theme appeared in work of Thurston, who used the geometry of Teichm├╝ller space to understand mapping class groups of surfaces.

For the group Out(Fn) of outer automorphisms of a free group, the geometric object which plays the role of a homogeneous space or Teichm├╝ller space is known as Outer space. This series of lectures will begin with a review of classical facts about automorphisms of free groups and the definition of Outer space, then explore analogies and direct connections between Out(Fn) and lattices and mapping class groups. We will discuss the geometry, combinatorics and topology of Outer space and its quotient moduli space of graphs, finiteness properties and cohomology of Out(Fn), dynamics of the action of Out(Fn) on Outer space and rigidity properties of Out(Fn).