Bridge number, Heegaard genus and non-integral dehn surgery

Kenneth L. Baker; Cameron Gordon; John Luecke

doi:10.1090/S0002-9947-2014-06328-9

Bridge number, Heegaard genus and non-integral dehn surgery

Kenneth L. Baker, Cameron Gordon, John Luecke

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 language	English (US)
Pages (from-to)	5753-5830
Number of pages	78
Journal	Transactions of the American Mathematical Society
Volume	367
Issue number	8
DOIs	https://doi.org/10.1090/S0002-9947-2014-06328-9
State	Published - 2015

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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AB - 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.

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