2-dimensional Coxeter groups are biautomatic

Coxeter groups are virtually special

In this paper we prove that every finitely generated Coxeter group has a finite index subgroup that is the fundamental group of a special cube complex. Some consequences include: Every f.g. Coxeter group is virtually a subgroup of a right-angled Coxeter group. Every word-hyperbolic Coxeter group has separable quasiconvex subgroups. © 2010 Elsevier Inc. All rights reserved. MSC: 53C23; 20F36; 20...

Three-generator Artin Groups of Large Type Are Biautomatic

In this article we construct a piecewise Euclidean, non-positively curved 2-complex for the 3-generator Artin groups of large type. As a consequence we show that these groups are biautomatic. A slight modification of the proof shows that many other Artin groups are also biautomatic. The general question (whether all Artin groups are biautomatic) remains open.

Rigidity of Two-dimensional Coxeter Groups

A Coxeter system (W, S) is called two-dimensional if the Davis complex associated to (W, S) is two-dimensional (equivalently, every spherical subgroup has rank less than or equal to 2). We prove that given a two-dimensional system (W, S) and any other system (W, S) which yields the same reflections, the diagrams corresponding to these systems are isomorphic, up to the operation of diagram twist...

Rational Subgroups of Biautomatic Groups

Central Quotients of Biautomatic Groups

The quotient of a biautomatic group by a subgroup of the center is shown to be biautomatic. The main tool used is the Neumann-Shapiro triangulation of S, associated to a biautomatic structure on Zn. As an application, direct factors of biautomatic groups are shown to be biautomatic. Biautomatic groups form a wide class of finitely presented groups with interesting geometric and computational pr...