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Gordon, Cameron McA and Montesinos Amilibia, José María
(1986)
*Fibred knots and disks with clasps.*
Mathematische Annalen, 275
(3).
pp. 405-408.
ISSN 0025-5831

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Official URL: http://link.springer.com/article/10.1007%2FBF01458613

## Abstract

It is known that every closed, orientable 3-manifold contains a fi-bered knot—a simple closed curve whose complement is a surface bundle over S1. For K such a fibered knot in a rational homology 3-sphere M it is shown that for any compact submanifold X of M containing K as a null-homologous subset, each component of ∂X is compressible in M−K. If K is a doubled knot (bounds a disk with one clasp) then it follows that K is a double of the trivial knot. More generally, it follows that the genus of X (minimum number of one-handles) is less than the genus of M.

Item Type: | Article |
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Uncontrolled Keywords: | null-homotopic knot in a closed, orientable 3-manifold; disk-with-clasps; fibred knot; null-homotopic in a handlebody of genus 2 |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 22089 |

Deposited On: | 26 Jun 2013 17:51 |

Last Modified: | 12 Dec 2018 15:14 |

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