Artin groups of Euclidean type

• 成果类型: Article
• 署名作者: McCammond, Jon; Sulway, Robert
• 署名单位: University of California System; University of California Santa Barbara
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0728-2
• 发表日期: 2017
• 页码: 231-282
• 关键词: k(pi

摘要

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 infinitet-ype 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.