Some knots in S1 × S2 with lens space surgeries

Kenneth Baker, Dorothy Buck, Ana G. Lecuona

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

We propose a classification of knots in S1 × S2 that admit a longitudinal surgery to a lens space. Any lens space obtainable by longitudinal surgery on some knot in S1 × S2 may be obtained from a Berge-Gabai knot in a Heegaard solid torus of S1 × S2, as observed by Rasmussen. We show that there are yet two other families of knots: those that lie on the fiber of a genus one fibered knot and the 'sporadic' knots. Assuming results of Cebanu, we are able to further conclude that these three families constitute all the doubly primitive knots in S1 × S2. Thus we bring the classification of lens space surgeries on knots in S1 × S2 in line with the Berge Conjecture about lens space surgeries on knots in S3.

Original languageEnglish (US)
Pages (from-to)431-470
Number of pages40
JournalCommunications in Analysis and Geometry
Volume24
Issue number3
StatePublished - 2016

ASJC Scopus subject areas

  • Statistics and Probability
  • Geometry and Topology
  • Analysis
  • Statistics, Probability and Uncertainty

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