Annette Karrer (Ohio State University)

Title: Subgroups arising from connected components in the Morse boundary.

Abstract: Every finitely generated group G has an associated topological space, called a Morse boundary, that captures the hyperbolic-like behavior of G at infinity. It was introduced by Cordes generalizing the contracting boundary invented by Charney-Sultan. In this talk, we study connected components of Morse boundaries. We introduce the notion of point-convergence and show that if the set of non-singleton connected components of the Morse boundary of a finitely generated group G is point-convergent, then every non-singleton connected component is the (relative) Morse boundary of its stabiliser. The above property only depends on the topology of the Morse boundary and hence is invariant under quasi-isometry. This shows that the Morse boundary can be used to detect certain subgroups which in some sense are invariant under quasi-isometry. This is joint work with Bobby Miraftab and Stefanie Zbinden.

After the talk, there will be board games in the lounge and then we will go for dinner.