An invariant of regular isotopy for disoriented links

Authors

İSMET ALTINTAŞ
HATİCE PARLATICI

DOI

10.55730/1300-0098.3345

Abstract

In this paper, we define a two-variable polynomial invariant of regular isotopy, $M_{K}$ for a disoriented link diagram $K$. By normalizing the polynomial $M_{K}$ using complete writhe, we obtain a polynomial invariant of ambient isotopy, $N_{K}$, for a disoriented link diagram $K$. The polynomial $N_{K}$ is a generalization of the expanded Jones polynomial for disoriented links and is an expansion of the Kauffman polynomial $F$ to the disoriented links. Moreover, the polynomial $M_{K}$ is an expansion of the Kauffman polynomial $L$ to the disoriented links.

Keywords

Disoriented link, disoriented crossing, disoriented regular isotopy, complete writhe, disoriented link polynomial

First Page

56

Last Page

74

Recommended Citation

ALTINTAŞ, İSMET and PARLATICI, HATİCE (2023) "An invariant of regular isotopy for disoriented links," Turkish Journal of Mathematics: Vol. 47: No. 1, Article 4. https://doi.org/10.55730/1300-0098.3345
Available at: https://journals.tubitak.gov.tr/math/vol47/iss1/4