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arXiv · 1407.6319

On possible existence of HOMFLY polynomials for virtual knots

Alexei Morozov·Andrey Morozov·Anton Morozov
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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.

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Alexei Morozov, Andrey Morozov, Anton Morozov. 2014-11-09. On possible existence of HOMFLY polynomials for virtual knots. https://doi.org/10.1016/j.physletb.2014.08.014

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