Bridge number, Heegaard genus and non-integral dehn surgery

Kenneth Baker, Cameron Gordon, John Luecke

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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
Volume367
Issue number8
DOIs
StatePublished - 2015

Fingerprint

Heegaard Splitting
Dehn Surgery
Surgery
Genus
Tunnels
Hyperbolic Knot
Tunnel
Intersect
Linear Function

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Bridge number, Heegaard genus and non-integral dehn surgery. / Baker, Kenneth; Gordon, Cameron; Luecke, John.

In: Transactions of the American Mathematical Society, Vol. 367, No. 8, 2015, p. 5753-5830.

Research output: Contribution to journalArticle

Baker, Kenneth ; Gordon, Cameron ; Luecke, John. / Bridge number, Heegaard genus and non-integral dehn surgery. In: Transactions of the American Mathematical Society. 2015 ; Vol. 367, No. 8. pp. 5753-5830.
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