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

Kenneth Baker, Tsuyoshi Kobayashi, Yo’Av Rieck

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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

Original languageEnglish (US)
Pages (from-to)3609-3618
Number of pages10
JournalProceedings of the American Mathematical Society
Volume144
Issue number8
DOIs
StatePublished - 2016

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Hyperbolic Knot
Tunnel
Tunnels

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Proceedings of the American Mathematical Society, Vol. 144, No. 8, 2016, p. 3609-3618.

Research output: Contribution to journalArticle

Baker, Kenneth ; Kobayashi, Tsuyoshi ; Rieck, Yo’Av. / The spectrum of the growth rate of the tunnel number is infinite. In: Proceedings of the American Mathematical Society. 2016 ; Vol. 144, No. 8. pp. 3609-3618.
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