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

Kenneth L. Baker, Tsuyoshi Kobayashi, Yo’Av Rieck

Research output: Contribution to journalArticle

1 Scopus citations

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 - Jan 1 2016

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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