Artin groups of euclidean type
Abstract
This article resolves several long-standing conjectures about Artin groups of euclidean type. In particular, 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.
Cite
@article{arxiv.1312.7770,
title = {Artin groups of euclidean type},
author = {Jon McCammond and Robert Sulway},
journal= {arXiv preprint arXiv:1312.7770},
year = {2017}
}
Comments
57 pages, 16 figures. Version 2 includes a proof that the euclidean Artin groups and dual euclidean Artin groups are isomorphic. Version 3 has minor corrections. To appear in the Inventiones Mathematicae