论文标题
Coxeter和Artin组的双重结构三个等级
Dual structures on Coxeter and Artin groups of rank three
论文作者
论文摘要
我们将双重Coxeter和Artin组的理论扩展到所有排名三的Coxeter系统，而不是先前研究的球形和仿射病例。使用几何，组合和拓扑技术，我们表明排名三的非交叉分区POSET是可脱落的晶格，并引起了Garside群体对相关的标准Artin组的同构。在此框架内，我们证明了$ k（π，1）$猜想，中心的琐碎性以及对排名第三个Artin组的问题的溶解度。我们的一些建筑适用于一般的Artin群体；我们希望他们能为$ K（π，1）$猜想和该地区的其他开放问题开发完整的解决方案。
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 $K(π, 1)$ 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 $K(π, 1)$ conjecture and other open problems in the area.
