### Abstract

We show there exists a linear function w: N → N with the following property. Let K be a hyperbolic knot in a hyperbolic 3–manifold M admitting a non-longitudinal S3 surgery. If K is put into thin position with respect to a strongly irreducible, genus g Heegaard splitting of M, then K intersects a thick level at most 2w(g) times. Typically, this shows that the bridge number of K with respect to this Heegaard splitting is at most w(g), and the tunnel number of K is at most w(g) + g − 1.

Original language | English (US) |
---|---|

Pages (from-to) | 5753-5830 |

Number of pages | 78 |

Journal | Transactions of the American Mathematical Society |

Volume | 367 |

Issue number | 8 |

DOIs | |

State | Published - 2015 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*367*(8), 5753-5830. https://doi.org/10.1090/S0002-9947-2014-06328-9

**Bridge number, Heegaard genus and non-integral dehn surgery.** / Baker, Kenneth; Gordon, Cameron; Luecke, John.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 367, no. 8, pp. 5753-5830. https://doi.org/10.1090/S0002-9947-2014-06328-9

}

TY - JOUR

T1 - Bridge number, Heegaard genus and non-integral dehn surgery

AU - Baker, Kenneth

AU - Gordon, Cameron

AU - Luecke, John

PY - 2015

Y1 - 2015

N2 - We show there exists a linear function w: N → N with the following property. Let K be a hyperbolic knot in a hyperbolic 3–manifold M admitting a non-longitudinal S3 surgery. If K is put into thin position with respect to a strongly irreducible, genus g Heegaard splitting of M, then K intersects a thick level at most 2w(g) times. Typically, this shows that the bridge number of K with respect to this Heegaard splitting is at most w(g), and the tunnel number of K is at most w(g) + g − 1.

AB - We show there exists a linear function w: N → N with the following property. Let K be a hyperbolic knot in a hyperbolic 3–manifold M admitting a non-longitudinal S3 surgery. If K is put into thin position with respect to a strongly irreducible, genus g Heegaard splitting of M, then K intersects a thick level at most 2w(g) times. Typically, this shows that the bridge number of K with respect to this Heegaard splitting is at most w(g), and the tunnel number of K is at most w(g) + g − 1.

UR - http://www.scopus.com/inward/record.url?scp=84929448381&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929448381&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-2014-06328-9

DO - 10.1090/S0002-9947-2014-06328-9

M3 - Article

VL - 367

SP - 5753

EP - 5830

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 8

ER -