标题： Milnor纤维化和定向拟阵 显示英文标题

标题： Milnor fibrations and oriented matroids

摘要： 我们引入了一个组合模型，用于复化实排列的Milnor纤维，该模型使用了定向拟阵。 这是一个偏序集拟纤维，这是第一作者最近引入的一个概念，其定义域是Salvetti复形的一个细分，该细分源于对偶定向拟阵复形的一个自然细分。 这产生了一个具体的有限正则CW复形，它与复化实排列的Milnor纤维同伦等价，并意味着复化实排列的Milnor纤维的同伦类型仅依赖于由其定向拟阵给出的底层组合结构。 此外，我们的构造适用于任何定向拟阵，而不考虑其实现性，因此我们为任何定向拟阵得到了一个组合Milnor纤维的概念。 显示英文摘要

摘要： We introduce a combinatorial model for the Milnor fibration of a complexified real arrangement using oriented matroids. It is a poset quasi-fibration, a notion recently introduced by the first author, whose domain is a subdivision of the Salvetti complex stemming from a natural subdivision of the dual oriented matroid complex. This yields a concrete finite regular CW complex which is homotopy equivalent to the Milnor fiber of the complexified real arrangement and implies that the homotopy type of the Milnor fiber of a complexified real arrangement only depends on the underlying combinatorial structure given by its oriented matroid. Moreover, our construction works for any oriented matroid, disregarding realizability, so we obtain a notion of a combinatorial Milnor fibration for any oriented matroid.