Topology Seminar (Introductory Talk): Introduction to Outer space

Seminar | November 13 | 2:10-3 p.m. | 740 Evans Hall

 Karen Vogtmann, University of Warwick

 Department of Mathematics

Outer space is a contractible space on which the group $Out(F_n)$ of outer sutomorphisms of a free group acts with finite stabiizers. It is analogous to the symmetric space of positive-definite quadratic forms, with its action by $GL(n,\mathbb Z)$ or the Teichmuller space of a surface, with its action by the mapping class group of the surface. I will define Outer space, then show how to find a "spine" whose quotient by the action is compact. The spine (and closely related spaces) will play a major role in the next talk.