English

An elementary fact about unlinked braid closures

Geometric Topology 2014-12-22 v3

Abstract

Let n be a positive integer. We provide a Khovanov homology proof of the following classical fact: If the closure of an n-strand braid is the n-component unlink, then the braid is trivial.

Cite

@article{arxiv.1309.0759,
  title  = {An elementary fact about unlinked braid closures},
  author = {J. Elisenda Grigsby and Stephan M. Wehrli},
  journal= {arXiv preprint arXiv:1309.0759},
  year   = {2014}
}

Comments

8 pp, 2 figs; We thank Tim Cochran for pointing out that Prop. 1 appeared in Thm. 4.1 of his "Non-trivial links and plats with trivial Gassner matrices," MATH PROC CAMBRIDGE (1996) prior to the work of Birman-Menasco that we cited in v2. We have revised the abstract and intro of our paper accordingly

R2 v1 2026-06-22T01:19:55.119Z