Obtaining genus 2 Heegaard splittings from Dehn surgery

Kenneth L. Baker, Cameron Gordon, John Luecke

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Let K′ be a hyperbolic knot in S3 and suppose that some Dehn surgery on K′ with distance at least 3 from the meridian yields a 3-manifold M of Heegaard genus 2. We show that if M does not contain an embedded Dyck's surface (the closed nonorientable surface of Euler characteristic -1), then the knot dual to the surgery is either 0-bridge or 1-bridge with respect to a genus 2 Heegaard splitting of M. In the case that M does contain an embedded Dyck's surface, we obtain similar results. As a corollary, if M does not contain an incompressible genus 2 surface, then the tunnel number of K′ is at most 2.

Original languageEnglish (US)
Pages (from-to)2471-2634
Number of pages164
JournalAlgebraic and Geometric Topology
Volume13
Issue number5
DOIs
StatePublished - Jul 5 2013

Keywords

  • Bridge number
  • Dehn surgery
  • Heegaard splitting

ASJC Scopus subject areas

  • Geometry and Topology

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