Virtual Knot Diagrams and the Witten-Reshetikhin-Turaev Invariant

Details Virtual Knot Diagrams and the Witten-Reshetikhin-Turaev Invariant Virtual Knot Diagrams and the Witten-Reshetikhin-Turaev Invariant

2004-07-23

arxiv.org/abs/math/0407407v6

Mathematics

Geometric Topology

30 pages, 39 figures v. 4 typos corrected

Scientific paper

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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