Evolution method and HOMFLY polynomials for virtual knots
High Energy Physics - Theory
2015-05-11 v1 Mathematical Physics
Geometric Topology
math.MP
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.
Keywords
Cite
@article{arxiv.1411.2569,
title = {Evolution method and HOMFLY polynomials for virtual knots},
author = {Ludmila Bishler and Alexei Morozov and Andrey Morozov and Anton Morozov},
journal= {arXiv preprint arXiv:1411.2569},
year = {2015}
}
Comments
28 pages