English

Crossing changes in closed 3-braid diagrams

Geometric Topology 2010-01-12 v1

Abstract

A crossing in a knot is nugatory if changing the crossing does not change the knot type. Using an invariant of certain types of closed 3-braid diagrams, we show that if a closed 3-braid contains a nugatory crossing then its braid index is one or two. This proves a special case of a conjecture on nugatory crossings due to Xiao-Song Lin.

Keywords

Cite

@article{arxiv.1001.1559,
  title  = {Crossing changes in closed 3-braid diagrams},
  author = {Chad Wiley},
  journal= {arXiv preprint arXiv:1001.1559},
  year   = {2010}
}

Comments

20 pages, 12 figures

R2 v1 2026-06-21T14:32:56.356Z