欧拉示性数与自由群自同构群的作用
代数拓扑
2018-03-16 v2 动力系统
几何拓扑
摘要
设 为连通可定向流形，其欧拉示性数 。记 为自由群自同构群中唯一的指数为 2 的子群。则 （从而特殊线性群 ）) 通过同胚在 上的任何群作用都是平凡的。这证实了针对这些流形与 Zimmer 纲领相关的一个猜想。
引用
@article{arxiv.1707.06788,
title = {Euler characteristics and actions of automorphism groups of free groups},
author = {Shengkui Ye},
journal= {arXiv preprint arXiv:1707.06788},
year = {2018}
}
备注
The article arXiv:1609.07699 is split into two parts. This is the first part. As suggested by the referee, the main result has been generalized to topological actions of automorphism group of free groups. The title is also changed. To appear in Algebraic and Geometric Topology