An invariant of regular isotopy for disoriented links

Abstract

: In this paper, we define a two-variable p olynomial i nvariant o f r egular i sotopy, M K f or a d isoriented 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 l inks. Moreover, the polynomial M K is an expansion of the Kauffman p olynomial L to the disoriented links.