The metric morse boundary

Matthew Cordes (Brandeis)

Abstract: I will introduce three new quasi-isometry invariants of geodesic metric spaces: the metric Morse boundary, the stable dimension, and the Morse capacity dimension. All three of these invariants are related to collections of Morse geodesics in the metric space. (A geodesic is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the geodesic.) In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan. In the case of a proper Gromov hyperbolic space the Morse boundary is the Gromov boundary, the stable dimension is the asymptotic dimension, and the Morse capacity dimension is the capacity dimension (defined by Buyalo) of its boundary. Time permitting I will also discuss some of these invariants in the cases of right-angled Artin groups, mapping class groups, and Teichmuller space.