Artin groups of Euclidean type
By Jon McCammond, Robert Sulway. 2013
68 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b7dde5b00816d1d0a53b874c2427f7d0d1af05bf
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In Computational Theory and Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Proof of the $$K(\pi , 1)$$ conjecture for affine Artin groups (2019, methodology): “n space Y W. In Section 6 we show that K W is a classifying space, even when [1;w] is not a lattice. Our proof makes use of the construction of braided crystallographic groups by McCammond and Sulway [MS17], a \Garside completion" of dual ane Artin groups. Theorem D (Theorem 6.6). For every ane”