Abstract. Recently, right-angled Artin groups have attracted much attention in geometric group theory. They have a rich structure of subgroups and nice algorithmic properties, and they give rise to cubical complexes with a variety of applications. This survey article is meant to introduce readers to these groups and to give an overview of the relevant literature.
As demonstrated by Croke and Kleiner, the visual boundary of a CAT(0) group is not well‐defined since quasi‐isometric CAT(0) spaces can have non‐homeomorphic boundaries. We introduce a new type of boundary for a CAT(0) space, called the contracting boundary, made up of rays satisfying one of five hyperbolic‐like properties. We prove that these properties are all equivalent and that the contracting boundary is a quasi‐isometry invariant. We use this invariant to distinguish the quasi‐isometry classes of certain right‐angled Coxeter groups.
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