Virtual Knot Diagrams and the Witten-Reshetikhin-Turaev Invariant
Geometric Topology
2009-07-15 v6
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.
Keywords
Cite
@article{arxiv.math/0407407,
title = {Virtual Knot Diagrams and the Witten-Reshetikhin-Turaev Invariant},
author = {H. A. Dye and Louis H. Kauffman},
journal= {arXiv preprint arXiv:math/0407407},
year = {2009}
}
Comments
30 pages, 39 figures v. 4 typos corrected