具有孤立平面的群的连通性性质与分裂
群论
2021-05-05 v3 几何拓扑
摘要
本文研究CAT(0)群及其作为群图的分裂。对于具有孤立平面的单端CAT(0)群，我们证明了一个定理，精确刻画了视觉边界何时是局部连通的。该刻画取决于群是否关于一个几乎阿贝尔子群具有某种类型的分裂。在局部连通的情形下，我们将边界描述为\'Swi\k{a}tkowski意义上的度量空间树。上述结果证明中使用的一个重要工具是关于任意CAT(0)群的一般凸分裂定理。若一个CAT(0)群分裂为具有凸边群的群图，则顶点群也是CAT(0)群。
引用
@article{arxiv.1705.00784,
title = {Connectedness properties and splittings of groups with isolated flats},
author = {G. Christopher Hruska and Kim Ruane},
journal= {arXiv preprint arXiv:1705.00784},
year = {2021}
}
备注
37 pages. The introduction has been substantially rewritten. A claimed result from an earlier version about the semistability of all CAT(0) groups with isolated flats has been removed because the proof contained an error. A correct proof of that result can be found in the article arXiv:1904.12947. Some theorem numbers may have changed