
Title: Regular Cube Complexes and Lieghton's Theorem
Speaker: Daniel Woodhouse (University of Oxford)
Abstract: I will discuss a large family of homogeneous CAT(0) cube complexes, previously studied by Lazarovich, which offer a natural generalization of regular graphs. I will then show how Leighton's graph covering theorem can be generalized to this setting. More precisely, given such a homogeneous CAT(0) cube complex X, covering two finite cube complexes X_1 and X_2, we will construct a common finite covering of X_1 and X_2. I will discuss potential applications to quasi-isometric rigidity.