有限复反射排列是K（pi，1）
Finite complex reflection arrangements are K(pi,1)
摘要：
设$V$是有限维复向量空间，$W\subseteq \GL(V)$是有限复反射群.令$V^{\reg}$是反射超平面的$V$中的补。证明了$V^{\reg}$是一个$K(π,1)$空间.这是预测的一个经典猜想，最初由Brieskorn复杂的真实反射群。复杂化的真实情况如下定理德利涅和贡献后，中村和奥利克所罗门，只有六个例外的情况下仍然开放。除了解决这六种情况下，我们的方法是适用于大多数以前已知的情况下，包括复杂的真正的群体，我们获得了一个新的证明，基于新的几何对象。我们还解决了一些关于$π_1(W\cq V^{\reg})$的问题，$W$的辫群。这包括用施普林格的规则元素理论的辫子模拟来描述周期元素。
英文摘要：
Let $V$ be a finite dimensional complex vector space and $W\subseteq \GL(V)$ be a finite complex reflection group. Let $V^{\reg}$ be the complement in $V$ of the reflecting hyperplanes. We prove that $V^{\reg}$ is a $K(π,1)$ space. This was predicted by a classical conjecture, originally stated by Brieskorn for complexified real reflection groups. The complexified real case follows from a theorem of Deligne and, after contributions by Nakamura and Orlik-Solomon, only six exceptional cases remained open. In addition to solving this six cases, our approach is applicable to most previously known cases, including complexified real groups for which we obtain a new proof, based on new geometric objects. We also address a number of questions about $π_1(W\cq V^{\reg})$, the braid group of $W$. This includes a description of periodic elements in terms of a braid analog of Springer's theory of regular elements.
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