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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 R{\cal R}-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}
}
R2 v1 2026-06-24T10:46:11.934Z