弱特殊方形复形的拟等距不变量
群论
2023-09-07 v6 几何拓扑
摘要
我们为紧致弱特殊方形复形的万有覆叠定义了交复形，并证明其为一个拟等距不变量。利用该拟等距不变量，我们研究了二维直角阿廷群与平面图 2-辫群的拟等距分类。我们的结果涵盖二维直角阿廷群的两个著名情形：（1）其定义图为树的情形；（2）其外自同构群为有限的情形。最后，我们证明存在无穷多个图 2-辫群拟等距于直角阿廷群，也存在无穷多个不拟等距于直角阿廷群。
引用
@article{arxiv.2009.03865,
title = {Quasi-isometry invariants of weakly special square complexes},
author = {Sangrok Oh},
journal= {arXiv preprint arXiv:2009.03865},
year = {2023}
}
备注
We have changed the terminology `special cacti' to `simplest cacti' since the previous definition was not enough to cover the results about graph 2-braid groups in the paper. The corrigendum will appear in Topology and its applications. This is a unified version of the previous paper and its corrigendum (everything appeared in the corrigendum has been corrected)