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Three-dimensional FC Artin groups are CAT(0). (English) Zbl 1134.20038
Summary: Building upon earlier work of T. Brady, we construct locally CAT(0) classifying spaces for those Artin groups which are three-dimensional and which satisfy the FC (flag complex) condition. The approach is to verify the ‘link condition’ by applying gluing arguments for CAT(1) spaces and by using the curvature testing techniques of M. Elder and J. McCammond [Exp. Math. 11, No. 1, 143-158 (2002; Zbl 1042.20030)].

MSC:
20F36 Braid groups; Artin groups
20F65 Geometric group theory
20F55 Reflection and Coxeter groups (group-theoretic aspects)
57M07 Topological methods in group theory
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