EXCEPTIONAL SURGERIES IN 3-MANIFOLDS

Kenneth L. Baker; Neil R. Hoffman

doi:10.1090/bproc/105

EXCEPTIONAL SURGERIES IN 3-MANIFOLDS

Kenneth L. Baker, Neil R. Hoffman

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	351-357
Number of pages	7
Journal	Proceedings of the American Mathematical Society, Series B
Volume	9
DOIs	https://doi.org/10.1090/bproc/105
State	Published - 2022
Externally published	Yes

Bibliographical note

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

Keywords

Exceptional surgeries
knots in handlebodies
toroidal fillings

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10.1090/bproc/105

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AU - Hoffman, Neil R.

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AB - 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.

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KW - knots in handlebodies

KW - toroidal fillings

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ER -

EXCEPTIONAL SURGERIES IN 3-MANIFOLDS

Abstract

Bibliographical note

Keywords

Publisher link

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