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arXiv · 1411.2569

Evolution method and HOMFLY polynomials for virtual knots

Ludmila Bishler·Alexei Morozov·Andrey Morozov·Anton Morozov
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Abstract

Following the suggestion of arXiv:1407.6319 to lift the knot polynomials for virtual knots and links from Jones to HOMFLY, we apply the evolution method to calculate them for an infinite series of twist-like virtual knots and antiparallel 2-strand links. Within this family one can check topological invariance and understand how differential hierarchy is modified in virtual case. This opens a way towards a definition of colored (not only cabled) knot polynomials, though problems still persist beyond the first symmetric representation.

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Ludmila Bishler, Alexei Morozov, Andrey Morozov, Anton Morozov. 2014-11-10. Evolution method and HOMFLY polynomials for virtual knots. https://doi.org/10.1142/s0217751x15500748

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