Abstract
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.
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Partial support by the National Science Foundation is gratefully acknowledged.
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McCammond, J., Sulway, R. Artin groups of Euclidean type. Invent. math. 210, 231–282 (2017). https://doi.org/10.1007/s00222-017-0728-2
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DOI: https://doi.org/10.1007/s00222-017-0728-2