## Abstract

A theorem of Jorgensen and Thurston implies that the volume of a hyperbolic 3-manifold is bounded below by a linear function of its Heegaard genus. Heegaard surfaces and bridge surfaces often exhibit similar topological behavior; thus it is natural to extend this comparison to ask whether a (g, b)-bridge surface for a knot K in S^{3} carries any geometric information related to the knot exterior. In this paper, we show that — unlike in the case of Heegaard splittings — hyperbolic volume and genus g-bridge numbers are completely independent. That is, for any g, we construct explicit sequences of knots with bounded volume and unbounded genus g-bridge number, and explicit sequences of knots with bounded genus g-bridge number and unbounded volume.

Original language | English |
---|---|

Pages (from-to) | 1805-1818 |

Number of pages | 14 |

Journal | Proceedings of the American Mathematical Society |

Volume | 145 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2017 |