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A study of subgroups of right-angled Coxeter groups via Stallings-like techniques

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Ivan Levcovitz (Technion)

Abstract:
Associated to any simplicial graph K is the right-angled Coxeter group (RACG) whose presentation consists of an order 2 generator for each vertex of K and relations stating that two generators commute if there is an edge between the corresponding vertices of K. RACGs contain a rich class of subgroups including, up to commensurability, hyperbolic 3-manifold groups, surface groups, free groups, Coxeter groups and right-angled Artin groups to name a few. I will describe a procedure which associates a cube complex to a given subgroup of RACG. I will then present some results regarding structural and algorithmic properties of subgroups of RACGs whose proofs follow from this viewpoint. This is joint work with Pallavi Dani.