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Artin groups of Euclidean type. (English) Zbl 1423.20032
Summary: This article resolves several long-standing conjectures about Artin groups of Euclidean type. Specifically we prove that every irreducible Euclidean Artin group is a torsion-free centerless group with a decidable word problem and a finite-dimensional classifying space. We do this by showing that each of these groups is isomorphic to a subgroup of a group with an infinite-type Garside structure. The Garside groups involved are introduced here for the first time. They are constructed by applying semi-standard procedures to crystallographic groups that contain Euclidean Coxeter groups but which need not be generated by the reflections they contain.

MSC:
20F36 Braid groups; Artin groups
20F55 Reflection and Coxeter groups (group-theoretic aspects)
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