论文标题
la猜想du $ k（π，1）$ pour les groupes d'Artin offines（d'AprèsPaoliniet salvetti）
La conjecture du $K(π,1)$ pour les groupes d'Artin affines (d'après Paolini et Salvetti)
论文作者
论文摘要
考虑一个由Isometries在Euclidean Space $ \ Mathbb {r}^n $上进行的Aggine Coxeter组$ W $，以及其反射超平面的安排。补充$ y_w $的基本组在$ \ mathbb {c}^n $ mod中由$ w $输出，是与$ w $相关的affine artin group $ g_w $。 $ k（π，1）$猜想指出，$ y_w $是$ g_w $的分类空间。 Paolini和Salvetti Building最近在麦卡蒙德（McCammond）和苏尔威（Sulway）的作品中证明了这一点。我们将提供一些证据的成分，这些成分基于对仿期Artin组的双Garside结构的研究，欧几里得异构体的分解以及非划分分区的可撒性。结果之一是，仿射型Artin组以及编织的晶体学组具有有限的分类空间。
Consider an affine Coxeter group $W$ acting by isometries on the Euclidean space $\mathbb{R}^n$, and the arrangement of its reflection hyperplanes. The fundamental group of the complement $Y_W$ of the complexification of this arrangement in $\mathbb{C}^n$ mod out by $W$ is the affine Artin group $G_W$ associated with $W$. The $K(π,1)$ conjecture states that $Y_W$ is a classifying space for $G_W$. It has been recently proved by Paolini and Salvetti building on the works of McCammond and Sulway. We will present some ingredients of the proof that rests on the study of dual Garside structures for affine Artin groups, the factorisations of Euclidean isometries, and the shellability of noncrossing partitions. One consequence is that affine Artin groups, as well as braided crystallographic groups, have a finite classifying space.
