Quasi-Isometries for certain Right-Angled Coxeter Groups

Abstract: We will introduce a construction of a specific graph of groups, the so-called JSJ tree of cylinders, for certain right-angled Coxeter groups (RACGs) in terms of the defining graph. We will use this as a tool in the hunt for a solution to the Quasi-Isometry Problem of certain RACGs, because if there is a quasi-isometry between two RACGs, there is an induced tree isomorphism between the respective JSJ trees of cylinders. In particular, this tree isomorphism preserves some additional structure of the JSJ tree of cylinders. With this fact at hand we can distinguish RACGs up to quasi-isometry. Additionally, we explain that in certain cases this structure preserving tree isomorphism even provides a complete quasi-isometry invariant.

algebraic topologyfunctional analysisgroup theorygeometric topologyoperator algebras

Audience: researchers in the topic

Vienna Geometry and Analysis on Groups Seminar