定量的 Birman-Menasco 有限性定理及其在交叉数上的应用
几何拓扑
2023-03-13 v3
摘要
Birman-Menasco 证明了具有给定亏格与辫指数的纽结只有有限多个。我们给出 Birman-Menasco 有限性定理的定量版本，即根据亏格与辫指数对纽结交叉数的估计。这在交叉数的各种应用中有用，例如连通和或卫星纽结的交叉数。
引用
@article{arxiv.2010.12150,
title = {A quantitative Birman-Menasco finiteness theorem and its application to crossing number},
author = {Tetsuya Ito},
journal= {arXiv preprint arXiv:2010.12150},
year = {2023}
}
备注
11 pages, 5 figures; v3. error in Proposition 2 is corrected. Main applications (Corollary 1-- 6) are not changed. v2. Corollary 6, an estimate for the crossing number of satellite knot, is added