Zachary Munro

The cubical geometry of small-cancellation groups

A CAT(0) cube complex is a nonpositively curved metric space built from identifying faces of Euclidean cubes. Small-cancellation groups are fundamental groups of 2-complexes satisfying a form of combinatorial non-positive curvature, and they are central examples in combinatorial and geometric group theory. Constructing actions of small-cancellation groups on CAT(0) cube complexes has yielded a number of strong separability properties, following work of Agol and Wise. We will discuss new results in both the negative and positive directions, i.e. showing certain small-cancellation groups are not cubulated and various others exhibit cube-like behavior.