Swiss Knots 2011

Knot Theory and Algebra

Lake Thun, May 23-27

Virtual Knots, Parity and Categorifications of the Arrow Polynomial

Prof. Dr. Louis H. Kauffman's talk
Date: 23.05.11   Time: 11.20 - 12.10   Room: Gwatt Zentrum

Coauthors: H. Dye, A. Kaestner, V.O. Manturov

Abstract: This talk is an introduction to virtual knot theory and some problems that are of particular interest to the speaker. We will discuss how there are virtual knots with unit Jones polynomial and how this leads to generalizations of the Jones polynomial that are particularly suited to knots in thickened surfaces and to virtual knots. In particular we discuss uses of parity in sharpening the Jones polynomial and uses of orientation (the arrow polynomial). We discuss how one can categorify the arrow polynomial (a natural generalization of the Jones polynomial using oriented diagrams) and the properties and limitations of these invariants.