On possible existence of HOMFLY polynomials for virtual knots

Abstract

Virtual knots are associated with knot diagrams, which are not obligatory planar. The recently suggested generalization from N=2 to arbitrary N of the Kauffman-Khovanov calculus of cycles in resolved diagrams can be straightforwardly applied to non-planar case. In simple examples we demonstrate that this construction preserves topological invariance -- thus implying the existence of HOMFLY extension of cabled Jones polynomials for virtual knots and links.

12 pages

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Cited by in corpus (3)

• On R-matrix approaches to knot invariants
• Planar decomposition of the HOMFLY polynomial for bipartite knots and links
• Evolution method and HOMFLY polynomials for virtual knots