On possible existence of HOMFLY polynomials for virtual knots
arXiv:1407.6319 · doi:10.1016/j.physletb.2014.08.014
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.
arXiv comment12 pages
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