### Abstract

For any ε > 0 we construct a hyperbolic knot K ⊂ S^{3} for which 1 − ε <gr_{t}(K) <1. This shows that the spectrum of the growth rate of the tunnel number is infinite.

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

Pages (from-to) | 3609-3618 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 144 |

Issue number | 8 |

DOIs | |

State | Published - 2016 |

### Fingerprint

### Keywords

- Heegaard splittings
- Knots
- Phrases. 3-manifold
- Tunnel number

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*144*(8), 3609-3618. https://doi.org/10.1090/proc/12957

**The spectrum of the growth rate of the tunnel number is infinite.** / Baker, Kenneth; Kobayashi, Tsuyoshi; Rieck, Yo’Av.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 144, no. 8, pp. 3609-3618. https://doi.org/10.1090/proc/12957

}

TY - JOUR

T1 - The spectrum of the growth rate of the tunnel number is infinite

AU - Baker, Kenneth

AU - Kobayashi, Tsuyoshi

AU - Rieck, Yo’Av

PY - 2016

Y1 - 2016

N2 - For any ε > 0 we construct a hyperbolic knot K ⊂ S3 for which 1 − ε t(K) <1. This shows that the spectrum of the growth rate of the tunnel number is infinite.

AB - For any ε > 0 we construct a hyperbolic knot K ⊂ S3 for which 1 − ε t(K) <1. This shows that the spectrum of the growth rate of the tunnel number is infinite.

KW - Heegaard splittings

KW - Knots

KW - Phrases. 3-manifold

KW - Tunnel number

UR - http://www.scopus.com/inward/record.url?scp=84969751450&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84969751450&partnerID=8YFLogxK

U2 - 10.1090/proc/12957

DO - 10.1090/proc/12957

M3 - Article

AN - SCOPUS:84969751450

VL - 144

SP - 3609

EP - 3618

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 8

ER -