有限群作用与 $\mathbf{S}^3$ 中纽结的循环分支覆盖
几何拓扑
2018-04-18 v3 群论
摘要
我们证明了双曲 -流形至多可以是 中十五个纽结的循环分支覆盖。这是关于作用于 -流形上的保定向微分同胚有限群的一般结果的推论。一个类似但较弱的结果对任意不可约 -流形成立：不可约 -流形至多可以是 中六个纽结的奇素数阶循环分支覆盖。
引用
@article{arxiv.1506.01895,
title = {Finite group actions and cyclic branched covers of knots in $\mathbf{S}^3$},
author = {Michel Boileau and Clara Franchi and Mattia Mecchia and Luisa Paoluzzi and Bruno Zimmermann},
journal= {arXiv preprint arXiv:1506.01895},
year = {2018}
}
备注
31 pages, 1 figure. Changes from v2: The paper has been substantially reorganized, in particular the proof of Theorem 2 was considerably shortened. Accepted for publication by the Journal of Topology