Freudenthal and Hopf introduced the notion of ends of groups and spaces and proved that a finitely generated group has 0, 1, 2, or infinitely many ends. Later Stallings proved that a finitely generated group has more than one end if and only if it acts minimally on a tree with finite edge stabilizers, so being one-ended is in some sense generic. We completely classify when the outer automorphism group of a finite free product of finite and cyclic groups has one end.
One-endedness of outer automorphism groups of free products of finite and cyclic groups
Rylee Alanza Lyman, Rutgers University–NewarkAuthors: Rylee Alanza Lyman
2023 AWM Research Symposium
Women in Groups, Geometry, and Dynamics [Organized by Hannah Hoganson and Rylee Lyman]