Quantum Topology

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Volume 5, Issue 4, 2014, pp. 523–539
DOI: 10.4171/QT/57

Published online: 2014-12-31

A graphical construction of the sl(3) invariant for virtual knots

Louis H. Kauffman[1] and Vassily O. Manturov[2]

(1) University of Illinois at Chicago, United States
(2) Bauman Moscow State Technical University, Russian Federation

We construct a graph-valued analogue of the Homypt sl(3) invariant for virtual knots. The restriction of this invariant for classical knots coincides with the usual Homypt sl(3) invariant, and for virtual knots and graphs it provides new information that allows one to prove minimality theorems and to construct new invariants for free knots. A novel feature of this approach is that some knots are of sufficient complexity that they evaluate themselves in the sense that the invariant is the knot itself seen as a combinatorial structure.

Keywords: Knot, link, virtual knot, graph, invariant, Kuperberg bracket, quantum invariant

Kauffman Louis, Manturov Vassily: A graphical construction of the sl(3) invariant for virtual knots. Quantum Topol. 5 (2014), 523-539. doi: 10.4171/QT/57