Arnold's seminar,
Moscow, May 17, 2005

Louis H Kauffman (UIC)
Introduction to Virtual Knot Theory

Abstract: Virtual knot theory is a stabilized theory of knots and links
embedded in thickened surfaces (S x I where S is a surface of genus g).
This theory has a diagrammatic expression very similar to the usual knot
diagrams for knots in the three-sphere. In virtual knot theory one adds an extra
crossing that is neither over nor under, and rules that are compatible
with the above interpretation of the theory. In a sense, virtual knot
theory is to classical knot theory as all graphs are to planar graphs.
Many phenomena appear in the virtual theory that are quite different
from the classical case. These include non-trivial  knots with unit Jones
polynomial. This talk is an introduction to the theory, and a discussion
of problems, results and new invariants and new ideas that arise from
this point of view. Many people have contributed to this field since its
onset in 1996. We shall touch on their work! Here is a short list of
the contributors: V.G. Bardakov, A. Bartholomew, S. Budden, S. Carter, D.
Bar-Natan,H. Dye, R. Fenn, R. Furmaniak, M. Gousssarov, J. Green, D. Hrencecin, D.
Jelsovsky, M. Jordan, L. Kauffman, T. Kadokami, N. Kamada, T. Kishino,
G. Kuperberg, M. Saito, D. Silver, S. Kamada, S. Lambropoulou, S. Nelson,
V. O. Manturov, D. E. Radford, M. Polyak, S. Satoh, J. Sawollek, W. Schellhorn,
V.V. Vershinin, O. Viro, S. Williams, P. Zinn-Justin and J. B. Zuber.

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