English

Exceptional surgeries in 3-manifolds

Geometric Topology 2021-09-02 v2

Abstract

Myers shows that every compact, connected, orientable 33--manifold with no 22--sphere boundary components contains a hyperbolic knot. We use work of Ikeda with an observation of Adams-Reid to show that every 33--manifold subject to the above conditions contains a hyperbolic knot which admits a non-trivial non-hyperbolic surgery, a toroidal surgery in particular. We conclude with a question and a conjecture about reducible surgeries.

Keywords

Cite

@article{arxiv.2101.12259,
  title  = {Exceptional surgeries in 3-manifolds},
  author = {Kenneth L. Baker and Neil R. Hoffman},
  journal= {arXiv preprint arXiv:2101.12259},
  year   = {2021}
}

Comments

5 pages, 3 figures, version 2 is supported by ancillary files which include certificates of computations done in sage. There are minor changes to the exposition to reference these files

R2 v1 2026-06-23T22:38:13.590Z