Three-generator Artin groups of large type are biautomatic

摘要

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. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: 20F32; 20F36; 57M07; 57M20. [References: 6]