PreprintarXiv licencearXiv
On Alternateness of the Jones-Kauffman Polynomial of Virtual Links
Abstract
We study alternateness of the Jones-Kauffman polynomial of virtual links. In particular, we identify a class of virtual links with alternating Jones-Kauffman polynomial that will be called the class of mock-alternating virtual links. Then, we explain how every mock-alternating virtual link can give rise to an infinite family of mock-alternating virtual links using the twisting technique introduced in [4] and later generalized in [5,18]. Finally, we give a connected state expansion of the mock-determinant for checkerboard-colorable links.
Related
- The colored Jones polynomial does not determine the Links--Gould polynomial
- The Colored Jones Function does not determine any colored Links--Gould polynomial
- On Khovanov homology of virtual links
- The Links--Gould polynomial of an alternating link is alternating
- Bridge numbers of virtual graphs and handlebody-links
BibTeX
@misc{abchir2026alternateness,
title = {{On Alternateness of the Jones-Kauffman Polynomial of Virtual Links}},
author = {Hamid Abchir and Khaled Qazaqzeh and Mohammed Sabak},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06752},
eprint = {2610.06752},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06752},
}
RIS
TY - UNPB
TI - On Alternateness of the Jones-Kauffman Polynomial of Virtual Links
AU - Hamid Abchir
AU - Khaled Qazaqzeh
AU - Mohammed Sabak
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06752
UR - https://arxiv.org/abs/2610.06752
AB - We study alternateness of the Jones-Kauffman polynomial of virtual links. In particular, we identify a class of virtual links with alternating Jones-Kauffman polynomial that will be called the class of mock-alternating virtual links. Then, we explain how every mock-alternating virtual link can give rise to an infinite family of mock-alternating virtual links using the twisting technique introduced in [4] and later generalized in [5,18]. Finally, we give a connected state expansion of the mock-determinant for checkerboard-colorable links.
ER -