Bridge number and integral Dehn surgery

Kenneth Baker, Cameron Gordon, John Luecke

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

In a 3–manifold M, let K be a knot and R be an annulus which meets K transversely. We define the notion of the pair (R, K) being caught by a surface Q in the exterior of the link K ∪ ∂ R. For a caught pair (R, K), we consider the knot Kn gotten by twisting Kn times along R and give a lower bound on the bridge number of Kn with respect to Heegaard splittings of M; as a function of n, the genus of the splitting, and the catching surface Q. As a result, the bridge number of Kn tends to infinity with n. In application, we look at a family of knots {Kn} found by Teragaito that live in a small Seifert fiber space M and where each Kn admits a Dehn surgery giving S3. We show that the bridge number of Kn with respect to any genus-2 Heegaard splitting of M tends to infinity with n. This contrasts with other work of the authors as well as with the conjectured picture for knots in lens spaces that admit Dehn surgeries giving S3

Original languageEnglish (US)
Pages (from-to)1-40
Number of pages40
JournalAlgebraic and Geometric Topology
Volume16
Issue number1
DOIs
StatePublished - Feb 23 2016

ASJC Scopus subject areas

  • Geometry and Topology

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