Modified right-angled Artin groups.

Abstract: The family of right-angled Artin groups (RAAGs) interpolates between the family of finitely generated free groups on one hand and the family of finitely generated free abelian groups on the other. RAAGs are easy to define (their definition can be encoded in a finite graph) and have very nice geometric and topological properties (they have non-positively curved cubical classifying spaces). There is a standard map from a RAAG to the integers, and the topological properties of the kernel is reflected in the topology of the clique complex associated to the defining finite graph. We introduce a new class of groups called modified RAAGs. Like classical RAAGs these can be encoded using finite graphs (with some extra decoration), and admit non-positively curved cubical classifying spaces. There are standard maps from modified RAAGs to the integers, and the kernels exhibit a wide range of geometric and topological properties. We will sketch the ideas involved in the construction of modified RAAGs, and will give some applications.