论文标题
关于非交叉分区晶格和Milnor纤维的同源性
On the homology of the noncrossing partition lattice and the Milnor fibre
论文作者
论文摘要
令$ \ Mathcal {l} $为与有限的Coxeter组$ W $相关的非交叉分区晶格。在本文中，我们为$ \ Mathcal {l} $的顶级同源组和等级选择的子镜头构建明确的基础。我们在基础上定义了$ \ Mathcal {l} $的惠特尼同源性的乘法结构，并且所得代数与Orlik-Solomon代数相似。作为一个应用程序，我们获得了四个连锁综合体，它们计算了$ W $反射安排的Milnor纤维的整体同源性，$ w $的判别物的Milnor纤维，$ W $的超平面补充和Artin类型$ W $。我们还对Milnor纤维的整体同源性进行了一些计算结果。
Let $\mathcal{L}$ be the noncrossing partition lattice associated to a finite Coxeter group $W$. In this paper we construct explicit bases for the top homology groups of intervals and rank-selected subposets of $\mathcal{L}$. We define a multiplicative structure on the Whitney homology of $\mathcal{L}$ in terms of the basis, and the resulting algebra has similarities to the Orlik-Solomon algebra. As an application, we obtain four chain complexes which compute the integral homology of the Milnor fibre of the reflection arrangement of $W$, the Milnor fibre of the discriminant of $W$, the hyperplane complement of $W$ and the Artin group of type $W$, respectively. We also tabulate some computational results on the integral homology of the Milnor fibres.
