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 language | English (US) |
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Pages (from-to) | 1-27 |
Number of pages | 27 |
Journal | Pacific Journal of Mathematics |
Volume | 305 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2020 |
Keywords
- Dehn surgery
- lens space
- Poincaré homology sphere
- tunnel number
ASJC Scopus subject areas
- Mathematics(all)