Affiliation:
1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, P. R. China
Abstract
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. 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.
Funder
General Research Project of Hunan Provincial Department of Education
Natural Science Foundation of Hunan Province
Doctor’s Funds of Xiangtan University
Hu Xiang Gao Ceng Ci Ren Cai Ju Jiao Gong Cheng–Chuang Xin Ren Cai
Publisher
World Scientific Pub Co Pte Ltd
Subject
Algebra and Number Theory