"Virtual Knot Theory"


( Louis H. Kauffman, (Universite d'Illinois, Chicago))


Abstract: 
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Virtual knot theory generalizes the classical theory of knots and
 links in three dimesional space to a theory of the combinatorial topology
of Gauss codes (symbolic patterns that encode knotting). Virtual knot
theory is described diagrammatically. Essentially all known quantum link
invariants ( and their
associated Vassiliev invariants) have extensions to the
virtual category.  Key examples are non-trivial virtual knots with unit
Jones polynomial   This talk will discuss work in progress on virtual knot 
theory and its relation to ideas in combinatorics and graph theory.