Abstract: Virtual knot theory is a study of embeddings of circles in thickend orientable surfaces. This is a particularly interesting case of knots in arbitrary three-manifolds. In the case of virtual knot theory, there is a corresponding diagrammatic theory that is remarkably similar to the familiar theory of knot diagrams for classical knots and links. As a result, it is possible to use a mixture of geometric and combinatorial topology to study virtual knots. There are many interesting phenomena and it is the intent of this talk to introduce some of these and to show how the Jones polynomial and its relatives fit into the virtual context.

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