English

The forbidden number of a knot

Geometric Topology 2018-08-14 v2

Abstract

Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the {\it forbidden number}. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.

Keywords

Cite

@article{arxiv.1305.5200,
  title  = {The forbidden number of a knot},
  author = {Alissa Crans and Sandy Ganzell and Blake Mellor},
  journal= {arXiv preprint arXiv:1305.5200},
  year   = {2018}
}

Comments

14 pages, many figures; v2 improves the upper bounds from the crossing number, and adds more detail to the data presented in the conclusion