超平面构形 Zaslavsky 定理的一种推广
组合数学
2014-03-04 v3 代数拓扑
摘要
我们定义了光滑流形中余维数为 1 的子流形构形，它推广了超平面构形。当这些子流形被移除后，流形分解为若干区域，每个区域都同胚于开圆盘。本文旨在推导计算此类构形所形成区域数目的公式。我们通过将 Zaslavsky 定理推广到这一情形来实现这一目标。我们证明了该数目由这些子流形之交的组合学性质所决定。
引用
@article{arxiv.1111.1251,
title = {On a Generalization of Zaslavsky's Theorem for Hyperplane Arrangements},
author = {Priyavrat Deshpande},
journal= {arXiv preprint arXiv:1111.1251},
year = {2014}
}
备注
version 3: The title had a typo in v2 which is now fixed. Will appear in Annals of Combinatorics. Version. 2: 19 pages, major revision in terms of style and language, some results improved, contact information updated, final version