双曲空间的诱导拟等距、马尔可夫链与凹状双曲性
群论
2025-01-08 v2 概率论
摘要
我们证明了（性质良好的）分层双曲群上的拟等距可降为它们极大双曲空间上的拟等距。这有两个应用：其一涉及凹状双曲性的拟等距不变性，其二为马尔可夫链的线性推进结果。附录由 Jacob Russell 撰写，在极大双曲空间为单端这一（必要）条件下给出了部分逆命题。
引用
@article{arxiv.2309.07013,
title = {Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity},
author = {Antoine Goldsborough and Mark Hagen and Harry Petyt and Jacob Russell and Alessandro Sisto},
journal= {arXiv preprint arXiv:2309.07013},
year = {2025}
}
备注
38 pages, 1 figure. Main paper by A. Goldsborough, M. Hagen, H. Petyt and A. Sisto; appendix by J. Russell. To appear in Groups, Geometry, and Dynamics