Year: 2024
Type: article
Abstract: We extend the theory of dual Coxeter and Artin groups to all rank-three Coxeter systems, beyond the previously studied spherical and affine cases.Using geometric, combinatorial, and topological techniques, we show that rank-three noncrossing partition posets are EL-shellable lattices and give rise to Garside groups isomorphic to the associated standard Artin groups.Within this framework, we prove the K. ; 1/ conjecture, the triviality of the center, and the solubility of the word problem for rank-three Artin groups.Some of our constructions apply to general Artin groups; we hope they will help develop complete solutions to the K. ; 1/ conjecture and other open problems in the area.
Source: Geometry & Topology
Authors: Emanuele Delucchi, Giovanni Paolini, Mario Salvetti
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4405922884