English

3-braid knots do not admit purely cosmetic surgeries

Geometric Topology 2021-02-17 v2

Abstract

A pair of surgeries on a knot is called purely cosmetic if the pair of resulting 3-manifolds are homeomorphic as oriented manifolds. Using recent work of Hanselman, we show that (nontrivial) knots which arise as the closure of a 3-stranded braid do not admit any purely cosmetic surgeries.

Keywords

Cite

@article{arxiv.2005.07278,
  title  = {3-braid knots do not admit purely cosmetic surgeries},
  author = {Konstantinos Varvarezos},
  journal= {arXiv preprint arXiv:2005.07278},
  year   = {2021}
}

Comments

10 pages, 3 figures; updated to avoid dependence on potentially unverified computational results

R2 v1 2026-06-23T15:33:41.412Z