Virtual Knot Theory and Detecting Knots with the Jones Polynomial
by
Louis H. Kauffman
University of Illinois at Chicago

Virtual Knot theory is a diagrammatic generalization of classical knot theory that articulates knots in thickened surfaces up to the addition and subtraction of empty 1-handles on the surface. Most classical invariants of knots and links generalize to the virtual category. This talk will consider a number of such generalizations, including the Jones polynomial, the Alexander polynomial, the fundamental group, the quandle and the biquandle. We will discuss the production of infinitely many non-trivial virtual knots with unit Jones polynomial, and the import of these constructions on the search for classical knots with unit Jones polynomial.

Date received: March 29, 2001