置换积与胖对角线的基本群和欧拉示性数
代数拓扑
2012-09-17 v2 代数几何
摘要
从拓扑和几何的角度研究了置换积及其各种“胖对角线”子空间。我们详细描述了与置换作用相关的稳定子群和轨道分层，给出了其深度的严格上界，然后特别关注了对角线分层的几何性质。我们写出了具有CW复形同伦型的连通空间的任意置换积的基本群表达式，该表达式用和表示。然后我们证明了上点配置空间（其中重数不超过）的基本群与一致。进一步的结果包括给出流形的胖对角线子空间再次成为流形的条件。文中包含了各种例子和同调计算。
引用
@article{arxiv.1010.1507,
title = {Fundamental Group and Euler Characteristic of Permutation Products and Fat Diagonals},
author = {Sadok Kallel and Walid Taamallah},
journal= {arXiv preprint arXiv:1010.1507},
year = {2012}
}
备注
The earlier version of this paper has now been split into two. Title change. The Euler characteristic computation will appear elsewhere. Many new details worked out in this new version, especially pertaining to section 3 on orbit stratifications and to the proof of main Theorem 1.1. Mistakes and mistatements corrected. 18 pages