3/10/2010

Daniel Wise
McGill University

CAT(0) cube complexes in geometric group theory

CAT(0) cube complexes are high-dimensional generalizations of trees that have emerged as increasingly central objects in combinatorial and geometric group theory. I will describe their prominent geometric properties and explain how cube complexes often arise from infinite groups - the latest examples being the fundamental groups of hyperbolic 3-manifolds. I'll then indicate a ``grand plan'' for understanding many groups from this viewpoint.