Penn Arts & Sciences Logo

Geometry-Topology Seminar

Monday, December 11, 2017 - 4:30pm

Catherine Pfaff

University of California Santa Barbara


University of Pennsylvania


While many fundamental contributions to the study of outer automorphisms of free groups date back to the early 20th century, the real explosion of activity in the field came with two much more recent developments: the definition by Culler and Vogtmann of the deformation space of metric graphs on a surface, namely Outer Space, and the development by Bestvina, Feighn, and Handel of a train track theory for outer automorphisms of free groups. The explosion was a result of a new ability to study free group outer automorphisms using generalizations of techniques developed to study surface homeomorphisms (mapping classes) via their action on the deformation space of metrics on the surface (Teichmuller space). In our talk, we focus specifically on a Nielsen-Thurston inspired story jointly studying:
1. outer automorphism conjugacy class invariants obtained by iteratively applying the automorphisms and
2. geodesics in Culler-Vogtmann Outer Space.