Three-generator Artin groups of large type are biautomatic. (English) Zbl 1004.20023

Brady, Thomas; McCammond, Jonathan P.

J. Pure Appl. Algebra 151, No. 1, 1-9 (2000).

Summary: 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.

MSC:

20F36	Braid groups; Artin groups
20F67	Hyperbolic groups and nonpositively curved groups
57M07	Topological methods in group theory
57M20	Two-dimensional complexes (manifolds) (MSC2010)

Keywords:

Artin groups; biautomatic groups

References:

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