论文标题
在接近三维流形的公制空间上的行动的刚度
Rigidity of actions on metric spaces close to three dimensional manifolds
论文作者
论文摘要
在本文中，我们提出了三个歧管的Zimmer程序的C^0 version的度量变化。在对几何三个字体的等轴测组进行了重新审查后，我们考虑在较高等级晶格上定义的同态，并在有限的图像或无限体积的商中建立二分法。在此过程中，我们列举了有限群体在可用的三个歧管上的作用的分类结果，并回答了Zimmer Zimmer计划的拓扑版本的标准差异，该计划是针对非球面三个歧管的拓扑版本（Weinberger and Ye）的要求，这些差异是基于这项工作和已知的拓扑性势态的二分法，这些二进制是针对三个平均差异。使用John Pardon和Galaz-García-Guijarro的结果，对于三个流形的等轴测组，高等级晶格的同态同态的二分法意味着，Zimmer程序的C 0-均衡版本对于与三个尺寸歧管的奇质空间密切相关，均与三个二维相关，而不是三二二元组，而不是三个二维或二维。 Zimmer程序的拓扑版本可以使用赦免的想法在Alexandrov空间的维度3中。
In this article we propose a metric variation on the C^0-version of the Zimmer program for three manifolds. After a reexamination of the isometry groups of geometric three-manifolds, we consider homomorphisms defined on higher rank lattices to them and establish a dichotomy betweeen finite image or infinite volume of the quotient. Along the way, we enumerate classification results for actions of finite groups on three manifolds where available, and we give an answer to a metric variation on topological versions of the Zimmer program for aspherical three manifolds, as asked by Weinberger and Ye, which are based on the dichotomy stablished in this work and known topological rigidity phenomena for three manifolds. Using results by John Pardon and Galaz-García-Guijarro, the dichotomy for homomorphisms of higher rank lattices to isometry groups of three manifolds implies that a C 0 -isometric version of the Zimmer program is also true for singular geodesic spaces closely related to three dimensional manifolds, namely three dimensional geometric orbifolds and Alexandrov spaces. A topological version of the Zimmer Program is seen to hold in dimension 3 for Alexandrov spaces using Pardon's ideas.
