论文标题
Milnor纤维同源综合体
Milnor fibre homology complexes
论文作者
论文摘要
令$ w $为有限的高级汽车组。我们给出一个代数介绍，以说明我们所说的``非交叉代数''，这与$ w $的超平面补体以及其Milnor纤维的共同体相关。这用于生产更简单，更一般的链（和科链）复合物，以计算$ W $的Milnor Fiber $ f $的积分同源性和同源组。在此过程中，我们定义了一个新的，较大的代数$ \ widetilde {a} $，它似乎是fomin-kirillov代数的``dual''，在低级中，它对它是线性的。 $ \ widetilde {a} $与Orlik-Solomon代数之间也存在着神秘的联系，与Fomin-Kirillov代数相比，Fomin-Kirillov代数包含$ w $的共依体代数。此分析用于计算$ \ langleρ，h^k（f，\ mathbb {c}）\ rangle_w $和$ \ langleρ，h^k（m，\ mathbb {c}） $ W $的代表。
Let $W$ be a finite Coxeter group. We give an algebraic presentation of what we refer to as ``the non-crossing algebra'', which is associated to the hyperplane complement of $W$ and to the cohomology of its Milnor fibre. This is used to produce simpler and more general chain (and cochain) complexes which compute the integral homology and cohomology groups of the Milnor fibre $F$ of $W$. In the process we define a new, larger algebra $\widetilde{A}$, which seems to be ``dual'' to the Fomin-Kirillov algebra, and in low ranks is linearly isomorphic to it. There is also a mysterious connection between $\widetilde{A}$ and the Orlik-Solomon algebra, in analogy with the fact that the Fomin-Kirillov algebra contains the coinvariant algebra of $W$. This analysis is applied to compute the multiplicities $\langle ρ, H^k(F,\mathbb{C})\rangle_W$ and $\langle ρ, H^k(M,\mathbb{C})\rangle_W$, where $M$ and $F$ are respectively the hyperplane complement and Milnor fibre associated to $W$ and $ρ$ is a representation of $W$.
