Geometry and Topology Seminar

Gromov boundary provides a useful compactification for all infinite-diameter Gromov hyperbolic spaces. It consists of all geodesic rays starting at a given base-point and it is an essential tool in the study of the coarse geometry of hyperbolic groups. In this talk we generalize the Gromov boundary. We first construct the sublinearly Morse boundaries and show that it is a QI-invariant, metrizable topological space. We show sublinearly Morse directions are generic both in the sense of Patterson-Sullivan and in the sense of random walk.  

The sublinearly Morse boundary is a subset of all directions with desired properties. In the second half we will truely consider the space of all directions and show that with some minimal assumptions on the space, the resulting boundary is a QI-invariant topology space in which many existing boundaries embeds. This talk is based on a series of work with Kasra Rafi and Giulio Tiozzo.