同痕不变量与Turaev亏格
几何拓扑
2021-02-22 v2
摘要
我们证明了纽结的各种同痕不变量（包括Rasmussen s-不变量及其推广的s_n-不变量）之间的差异给出了Turaev亏格的下界。利用我们的界对某些拟交错纽结非平凡这一事实，我们证明了某一类纽结的Turaev亏格的可加性。这导致我们首次得到对于任意固定正整数g，Turaev亏格恰好为g的拟交错纽结的无穷族，解决了Champanerkar-Kofman的一个问题。
引用
@article{arxiv.2010.00031,
title = {Concordance invariants and the Turaev genus},
author = {Hongtaek Jung and Sungkyung Kang and Seungwon Kim},
journal= {arXiv preprint arXiv:2010.00031},
year = {2021}
}
备注
6 pages, 3 figures. Some references are added or corrected. More descriptions on oriented band surgeries and slice-torus invariants are added