On the Kauffman-Vogel and the Murakami-Ohtsuki-Yamada Graph Polynomials

Abstract: This paper consists of three parts. First, we generalize the Jaeger Formula to express the Kauffman-Vogel graph polynomial as a state sum of the Murakami-Ohtsuki-Yamada graph polynomial. Then, we demonstrate that reversing the orientation and the color of a MOY graph along a simple circuit does not change the sl(N) Murakami-Ohtsuki-Yamada polynomial or the sl(N) homology of this MOY graph. In fact, reversing the orientation and the color of a component of a colored link only changes the sl(N) homology by an overall grading shift. Finally, as an application of the first two parts, we prove that the so(6) Kauffman polynomial is equal to the 2-colored sl(4) Reshetikhin-Turaev link polynomial, which implies that the 2-colored sl(4) link homology categorifies the so(6) Kauffman polynomial.