Séance Séminaire

Séminaire Gaston Darboux

Rough CAT(0) spaces and groups

In the talk I will be discussing rough CAT(0) spaces, or rCAT(0) in short, introduced by Buckley and myself, in an attempt to unify CAT(0)-theory and Gromov hyperbolicity, with special emphasis on boundary theory. When defining the boundary of a rCAT(0) space, bouquets of short segments, a concept related to Vaisala's roads, replace the classical geodesic rays to infinity known from the definition of the ideal boundary of a metric space. However, rCAT(0) spaces come in three flavours of which only the strongest allows a meaningful boundary theory, and the weakest turns out to be already known as so-called bolic spaces. As of now, we do not know whether these three conditions are equivalent or not. In the last part of the talk I will concentrate on rCAT(0) groups.