One conjecture on cut points of virtual links and the arrow polynomial of twisted links
One conjecture on cut points of virtual links and the arrow polynomial of twisted links
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虚拟链路割点与扭曲链路箭头多项式的一种猜想
DOI：
10.1142/s0218216522500663
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发表时间：
2021
影响因子：
0.5
通讯作者：
Qingying Deng
中科院分区：
文献类型：
--
作者：
Qingying Deng
棋盘格框架是虚拟链接棋盘格着色的扩展。根据棋盘框架，在2017年，Dye获得了虚拟链接的独立不变量：割点数。模板框架和切割点可以用作将其他经典不变量扩展到虚拟链接的工具。我们证明了Dye文章中的一个结论是正确的。分析了由虚拟链路图通过调整割点得到的棋盘格框架与由虚拟链路图通过引入条得到的扭链路图之间的联系与区别。通过调整虚链路的归一化箭头多项式，将其推广到扭链路。我们证明了它是扭链的不变量。最后给出了棋盘可染扭杆的归一化箭多项式的三个特征，这是检验扭杆棋盘可染性的一个工具。后两个特征与棋盘可着色虚拟链接图的情况相同。
Checkerboard framings are an extension of checkerboard colorings for virtual links. According to checkerboard framings, in 2017, Dye obtained an independent invariant of virtual links: the cut point number. Checkerboard framings and cut points can be used as a tool to extend other classical invariants to virtual links. We prove that one of the conjectures in Dye's paper is correct. Moreover, we analyze the connection and difference between checkerboard framing obtained from virtual link diagram by adapting cut points and twisted link diagram obtained from virtual link diagram by introducing bars. By adjusting the normalized arrow polynomial of virtual links, we generalize it to twisted links. And we show that it is an invariant for twisted link. Finally, we figure out three characteristics of the normalized arrow polynomial of a checkerboard colorable twisted link, which is a tool of detecting checkerboard colorability of a twisted link. The latter two characteristics are the same as in the case of checkerboard colorable virtual link diagram.