Detecting hyperbolicity in CAT(0) spaces: from cube complexes to rank rigidity

Abstract: CAT(0) spaces form a classical and well-studied class of spaces exhibiting non-positive curvature behaviour. An important subclass of CAT(0) spaces are CAT(0) cube complexes, i.e. spaces obtained by gluing Euclidean n-cubes along faces, satisfying some additional combinatorial conditions. Given a CAT(0) cube complex, there are several techniques to construct spaces that "detect the hyperbolic behaviour" of the cube complex, but all of those techniques rely on the combinatorial structure coming from the cubes. In this talk we will present a new approach to construct such spaces that works for general CAT(0) spaces, allowing us to make progress towards the rank-rigidity conjecture for CAT(0) spaces. This is joint work with H. Petyt and A. Zalloum.

group theoryrings and algebras

Audience: researchers in the topic

Al@Bicocca take-away