Exceptional surgeries in 3 -manifolds

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...

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Veröffentlicht in:Proceedings of the American Mathematical Society. Series B 2022-08, Vol.9 (33), p.351-357
Hauptverfasser: Baker, Kenneth L., Hoffman, Neil R.
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:2330-1511
2330-1511
DOI:10.1090/bproc/105