EXCEPTIONAL SURGERIES IN 3-MANIFOLDS

Kenneth L. Baker, Neil R. Hoffman

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Myers shows that every compact, connected, orientable 3-manifold with no 2-sphere boundary components contains a hyperbolic knot. We use work of Ikeda with an observation of Adams-Reid to show that every 3-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.

Original languageEnglish (US)
Pages (from-to)351-357
Number of pages7
JournalProceedings of the American Mathematical Society, Series B
Volume9
DOIs
StatePublished - 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022 by the author(s).

Keywords

  • Exceptional surgeries
  • knots in handlebodies
  • toroidal fillings

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