Professor: Louis H Kauffman, Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago |

Title:Graphical Invariants of Knots and Links |

Abstract:This talk is joint work with Qingying Deng. We generalize the signed Tutte polynomial relationship with the Kauffman bracket model of the Jones polynomial to a new polynomial defined on signed cyclic graphs (graphs with signed edges and cyclic orders at the vertices) and show how these graphs are codings for checkerboard colorable virtual links. We show how virtualization of classical links corresponds to simple operations on the planar signed cyclic graphs. We relate our new polynomial invariant to both the bracket polynomials for virtual knots and links and to the Bollobas-Riordan polynomial. |