二桥纽结的Ohtsuki-Riley-Sakuma偏序的上界
几何拓扑
2011-01-24 v2
摘要
本文利用连分数研究由Ohtsuki、Riley和Sakuma的工作导出的二桥纽结集合上的一个偏序。我们建立了任意二桥纽结集合在该偏序下存在上界的充要条件。此外，对于任意给定的二桥纽结K，我们刻画了所有使得集合{K, J}存在上界的其他二桥纽结J。作为应用，我们回答了Suzuki的一个问题，证明了由三叶结和八字结组成的集合不存在上界。
引用
@article{arxiv.1007.3278,
title = {Upper bounds in the Ohtsuki-Riley-Sakuma partial order on 2-bridge knots},
author = {Scott M. Garrabrant and Jim Hoste and Patrick D. Shanahan},
journal= {arXiv preprint arXiv:1007.3278},
year = {2011}
}
备注
21 pages, 2 figures. This is a significant revision of the paper "Two-bridge knots with common ORS covers," including a proof of Conjecture 1. We have retitled the paper and added an author