Cannon-Thurston maps for the Morse boundary

Fundamental to the study of hyperbolic groups is their Gromov boundaries. The classical Cannon--Thurston map for a closed fibered hyperbolic 3-manifolds relates two such boundaries: it gives a continuous surjection from the boundary of the surface group (a circle) to the boundary of the 3-manifold group (a 2-sphere). Mj (Mitra) generalized this to all hyperbolic groups with hyperbolic normal subgroups. A generalization of the Gromov boundary to all finitely generated groups is called the Morse boundary. It collects all the "hyperbolic-like" rays in a group. In this talk we will discuss Cannon--Thurston maps for Morse boundaries. This is joint work with Ruth Charney, Antoine Goldsborough, Alessandro Sisto and Stefanie Zbinden.