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Non-positively curved aspects of Artin groups of finite type. (English) Zbl 0998.20034
Summary: Artin groups of finite type are not as well understood as braid groups. This is due to the additional geometric properties of braid groups coming from their close connection to mapping class groups. For each Artin group of finite type, we construct a space (simplicial complex) analogous to Teichmüller space that satisfies a weak nonpositive curvature condition and also a space “at infinity” analogous to the space of projective measured laminations. Using these constructs, we deduce several group-theoretic properties of Artin groups of finite type that are well-known in the case of braid groups.

MSC:
20F36 Braid groups; Artin groups
20F65 Geometric group theory
20F67 Hyperbolic groups and nonpositively curved groups
57M07 Topological methods in group theory
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