当前位置: X-MOL 学术J. Topol. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Bordifications of hyperplane arrangements and their curve complexes
Journal of Topology ( IF 0.8 ) Pub Date : 2021-03-21 , DOI: 10.1112/topo.12184
Michael W. Davis 1 , Jingyin Huang 1
Affiliation  

The complement of an arrangement of hyperplanes in C n has a natural bordification to a manifold with corners formed by removing (or “blowing up”) tubular neighborhoods of the hyperplanes and certain of their intersections. When the arrangement is the complexification of a real simplicial arrangement, the bordification closely resembles Harvey's bordification of moduli space. We prove that the faces of the universal cover of the bordification are parameterized by the simplices of a simplicial complex C , the vertices of which are the irreducible “parabolic subgroups” of the fundamental group of the arrangement complement. So, the complex C plays a similar role for an arrangement complement as the curve complex does for moduli space. Also, in analogy with curve complexes and with spherical buildings, we prove that C has the homotopy type of a wedge of spheres. Our results apply in particular to spherical Artin groups, where the associated arrangement is a reflection arrangement of a finite Coxeter group.

中文翻译:

超平面排列的波状化及其曲线复合体

关于超平面排列的补充 C ñ 对具有歧管的流形具有自然的修饰,该歧管具有通过去除(或“吹起”)超平面的管状邻域及其某些相交点而形成的角。当这种安排是一个实际的简单安排的复杂化时,该协调非常类似于Harvey的模空间协调。我们证明了通用化掩盖的面孔是由单纯复形的简化参数化的 C ,其顶点是该安排补集的基本组的不可约的“抛物线子组”。所以,复杂 C 对于排列补码起着类似的作用,就像曲线复数对模空间一样。同样,类似于曲线复合体和球形建筑物,我们证明了 C 具有球面楔形的同伦类型。我们的结果尤其适用于球形Artin组,其中相关的排列是有限Coxeter组的反射排列。
更新日期:2021-03-22
down
wechat
bug