Evolution for Khovanov polynomials for figure-eight-like family of knots
Mathematical Physics
2019-10-31 v3 High Energy Physics - Theory
math.MP
Abstract
We look at how evolution method deforms, when one considers Khovanov polynomials instead of Jones polynomials. We do this for the figure-eight-like knots (also known as 'double braid' knots, see arXiv:1306.3197) -- a two-parametric family of knots which "grows" from the figure-eight knot and contains both two-strand torus knots and twist knots. We prove that parameter space splits into four chambers, each with its own evolution, and two isolated points. Remarkably, the evolution in the Khovanov case features an extra eigenvalue, which drops out in the Jones (t -> -1) limit.
Keywords
Cite
@article{arxiv.1812.00858,
title = {Evolution for Khovanov polynomials for figure-eight-like family of knots},
author = {Petr Dunin-Barkowski and Aleksandr Popolitov and Svetlana Popolitova},
journal= {arXiv preprint arXiv:1812.00858},
year = {2019}
}
Comments
9 pages, add some missing references