English

Normal and Jones surfaces of knots

Geometric Topology 2018-03-26 v4 Quantum Algebra

Abstract

We describe a normal surface algorithm that decides whether a knot, with known degree of the colored Jones polynomial, satisfies the Strong Slope Conjecture. We also discuss possible simplifications of our algorithm and state related open questions. We establish a relation between the Jones period of a knot and the number of sheets of the surfaces that satisfy the Strong Slope Conjecture (Jones surfaces). We also present numerical and experimental evidence supporting a stronger such relation which we state as an open question.

Keywords

Cite

@article{arxiv.1702.06466,
  title  = {Normal and Jones surfaces of knots},
  author = {Efstratia Kalfagianni and Christine Ruey Shan Lee},
  journal= {arXiv preprint arXiv:1702.06466},
  year   = {2018}
}

Comments

15 pages, 1 Figures and 1 Table. J. of knot Theory and Ramifications, to appear