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