THE POINCARÉ HOMOLOGY SPHERE, LENS SPACE SURGERIES, AND SOME KNOTS WITH TUNNEL NUMBER TWO

Kenneth L. Baker, Neil R. Hoffman

Research output: Contribution to journalArticlepeer-review

Abstract

We exhibit an infinite family of knots in the Poincare homology sphere with tunnel number 2 that have a lens space surgery. Notably, these knots are not doubly primitive and provide counterexamples to a few conjectures. Additionally, we update (and correct) our earlier work on Hedden’s almost-simple knots. In the appendix, it is shown that a hyperbolic knot in the Poincare homology sphere with a lens space surgery has either no symmetries or just a single strong involution.

Original languageEnglish (US)
Pages (from-to)1-27
Number of pages27
JournalPacific Journal of Mathematics
Volume305
Issue number1
DOIs
StatePublished - Mar 2020

Keywords

  • Dehn surgery
  • lens space
  • Poincaré homology sphere
  • tunnel number

ASJC Scopus subject areas

  • Mathematics(all)

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