由自旋与旋转族产生的自由积
几何拓扑
2022-01-05 v3 群论
摘要
Dahmani-Guirardel-Osin 的深远影响工作以及 Clay-Mangahas-Margalit 近期的工作提供了研究环境群 中子群（或子群集合）正规闭包的几何方法。他们的工作给出了 中正规闭包为自由积的条件。在本文中，我们统一了他们的结果，并简化且大幅缩短了 Dahmani-Guirardel-Osin 定理的证明。
引用
@article{arxiv.2010.10735,
title = {Free products from spinning and rotating families},
author = {Mladen Bestvina and Ryan Dickmann and George Domat and Sanghoon Kwak and Priyam Patel and Emily Stark},
journal= {arXiv preprint arXiv:2010.10735},
year = {2022}
}
备注
22 pages, 8 figures. Further simplified and shortened main proofs. Also added proofs that elements in the group generated by a spinning/rotating family either act loxodromically or are contained in a point stabilizer \'a la DGO and CMM. Added referee comments. Accepted to l`Enseignement Math\'{e}matique