Title: From Stallings' Theorem to connected components of Morse boundaries of graph of groups
Speaker: Annette Karrer (Ohio State University)
Abstract: Every finitely generated group G has an associated topological space, called a Morse boundary. It was introduced by a combination of Charney--Sultan and Cordes and captures the hyperbolic-like behavior of G at infinity.
In this talk, I will motivate the study of Morse boundaries with Stallings' theorem. We will formulate a variant of Stallings' theorem for Gromov boundaries of Gromov-hyperbolic groups. As Morse boundaries generalize Gromov boundaries, this raises the question whether it is possible to formulate an analog for Morse boundaries. Motivated by this question, we will study connected components of Morse boundaries of graph of groups. We will focus on the case where the edge groups are undistorted and do not contribute to the Morse boundary of the ambient group. Results presented are joint with Elia Fioravanti.
