Bridge number, Heegaard genus and non-integral dehn surgery

Kenneth L. Baker, Cameron Gordon, John Luecke

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 languageEnglish (US)
Pages (from-to)5753-5830
Number of pages78
JournalTransactions of the American Mathematical Society
Issue number8
StatePublished - 2015

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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