关于曲面群图的拟等距刚性
群论
2023-06-13 v2 几何拓扑
摘要
设 为一个字双曲群，具有一个仅含刚性顶点群的循环 JSJ 分解，且这些顶点群均为闭曲面群的基本群。我们证明任何与 拟等距的群 均与 抽象可公度。
引用
@article{arxiv.1904.10482,
title = {On the quasi-isometric rigidity of graphs of surface groups},
author = {Alexander Taam and Nicholas W. M. Touikan},
journal= {arXiv preprint arXiv:1904.10482},
year = {2023}
}
备注
After some revisions, the referee identified a gap in the proof of Lemma 4.20. The following results are impacted: Corollary 4.28, Corollary 5.19, and Theorem A. The authors believe that Corollary 4.28 may be false. What can be recovered from Sections 5 and 6 is that Churro-Waffle spaces are action rigid. The authors still believe that Theorem A is true and are currently working on another proof