Introduction to Virtual Knot Theory
报告题目(Title)： Introduction to Virtual Knot Theory
报告人(Speaker)：Louis H. Kauffman （University of Illinois at Chicago）
地点(Place)：后主楼 1124
时间(Time)：3月8日16:00-17:00
邀请人(Inviter)：程志云
报告摘要
Virtual knot theory studies the knot theory of embeddings of circles in thickened surfaces. By taking projections of the knot diagrams in surfaces to the plane one obtains a theory of diagrams that contain classical knot crossings and virtual crossings that are neither over nor under. The virtual crossings are an artifact of the projection of the knot to the plane but are very usefully for the combinatorial topology. Virtual crossings also occur in planar projections of non-planar graphs, and there are many analogies between graph theory and knot theory in this domain. The talk will discuss invariants of virtual knots such as the Jones polynomial in Kauffman bracket form, Manturov Parity Bracket, Arrow polynomial, Affine Index Polynomial and polynomials for signed cyclic graphs that are related to virtual knots and links. This theory has many interesting examples and many relations with classical knot theory and with combinatorics and graph theory. The talk will be self-contained.
