Evolution properties of the knot's defect
High Energy Physics - Theory
2022-09-21 v1 Mathematical Physics
Geometric Topology
math.MP
Abstract
The defect of differential (cyclotomic) expansion for colored HOMFLY-PT polynomials is conjectured to be invariant under any antiparallel evolution and change linearly with the evolution in any parallel direction. In other words, each -matrix can be substituted by an entire 2-strand braid in two different ways: the defect remains intact when the braid is antiparallel and changes by half of the added length when the braid is parallel.
Cite
@article{arxiv.2204.05977,
title = {Evolution properties of the knot's defect},
author = {A. Morozov and N. Tselousov},
journal= {arXiv preprint arXiv:2204.05977},
year = {2022}
}