Inventiones mathematicae

, Volume 210, Issue 1, pp 231–282 | Cite as

Artin groups of Euclidean type

  • Jon McCammond
  • Robert Sulway


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.

Mathematics Subject Classification



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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaSanta BarbaraUSA
  2. 2.DenverUSA

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