Virtual knot theory
by
Louis H. Kauffman
University of Illinois at Chicago
Coauthors: Heather Dye

Virtual knot theory constitutes the study of knots and links in thickened surfaces up to handle stabilization (one allows the addition and subtraction of empty 1-handles from the thickened surface). This theory admits a diagrammatic formulation that generalizes the Reidemeister moves for classical links. Many invariants of classical links extend to virtuals and new phenomena arise. This talk will survey recent work of the speaker and work in collaboration with Heather Dye.

We will discuss detection of virtual knots with unit Jones polynomial using both combinatorial and geometric techniques.

Date received: February 20, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajz-39.