An invariant of regular isotopy for disoriented links

Authors: İSMET ALTINTAŞ, HATİCE PARLATICI

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

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