Virtual Knot Diagrams and the Witten-Reshetikhin-Turaev Invariant

H. A. Dye; Louis H. Kauffman

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Virtual Knot Diagrams and the Witten-Reshetikhin-Turaev Invariant

H. A. Dye·Louis H. Kauffman

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Abstract

The Witten-Reshetikhin-Turaev invariant of classical link diagrams is generalized to virtual link diagrams. This invariant is unchanged by the framed Reidemeister moves and the Kirby calculus. As a result, it is also an invariant of the 3-manifolds represented by the classical link diagrams. This generalization is used to demonstrate that there are virtual knot diagrams with a non-trivial Witten-Reshetikhin-Turaev invariant and trivial 3-manifold fundamental group.

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BibTeX RIS

H. A. Dye, Louis H. Kauffman. 2004-11-17. Virtual Knot Diagrams and the Witten-Reshetikhin-Turaev Invariant. https://arxiv.org/abs/math/0407407

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