A dynamic interplay between conjugacy class invariants for outer automorphism groups of free groups and geodesics in outer space

Catherine Pfaff (UCSB)

Abstract: Mosher and Handel defined several conjugacy class invariants for outer automorphisms of free groups. These invariants record, with various levels of detail, the behavior of these automorphisms applied iteratively. In our dual programs of understanding these invariants and understanding the action of the outer automorphism group as an isometry group, we analyze the geometric implications of these invariants and then what the geometric implications say about the outer automorphisms with the invariants. Various pieces of this work are joint with Yael Algom-Kfir, Ilya Kapovich, and Lee Mosher.