Turkish Journal of Mathematics
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.
DOI
10.55730/1300-0098.3345
Keywords
Disoriented link, disoriented crossing, disoriented regular isotopy, complete writhe, disoriented link polynomial
First Page
56
Last Page
74
Recommended Citation
ALTINTAŞ, İ, & PARLATICI, H (2023). An invariant of regular isotopy for disoriented links. Turkish Journal of Mathematics 47 (1): 56-74. https://doi.org/10.55730/1300-0098.3345
