### 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) |
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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 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Bridge number, Heegaard genus and non-integral dehn surgery'. Together they form a unique fingerprint.

## Cite this

Baker, K., Gordon, C., & Luecke, J. (2015). Bridge number, Heegaard genus and non-integral dehn surgery.

*Transactions of the American Mathematical Society*,*367*(8), 5753-5830. https://doi.org/10.1090/S0002-9947-2014-06328-9