The Reserch Of Invariant For Virtual Knots

Louis H. Kauffman proved that an affine index polynomial of virtual knots is a kind 3f invariant. In section 2 of this paper, we offer a new polynomial Pk=∑sgn(c)(tWK(c)-1) and define it as pseudo affine index polynomial, following the method of Kauffman’s definition. In addition, we show that this polynomial is invariant only under the Reide-meister move2 and Reidemeister move3, so it is a kind of half invariant. Furthermore, we make an investigation of its properties.Zhiyun Cheng proved that there is an odd writhe polynomial of every virtual knot, and it is a kind of invariant for Z[t, t-1]. In the section 3 of this paper, under the con-dition of keeping the orientation of Gauss circle, we similarly get a kind of odd writhe polynomial fK(t)=∑ω(ci)tN(ci) following the method of the definition in document , which is still invariant. At the same time, we also get some properties that are similar to the document.