2-dimensional Coxeter groups are biautomatic. Issue 2 (April 2022) - Munro, Zachary; Osajda, Damian; Przytycki, Piotr
Abstract : Let W be a 2-dimensional Coxeter group, that is, one with 1/ m st + 1/ m sr + 1/ m tr ≤ 1 for all triples of distinct s, t, r ∈ S . We prove that W is biautomatic. We do it by showing that a natural geodesic language is regular (for arbitrary W ), and satisfies the fellow traveller property. As a consequence, by the work of Jacek Świątkowski, groups acting properly and cocompactly on buildings of type W are also biautomatic. We also show that the fellow traveller property for the natural language fails for W=A_3 .