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) |
|---|---|
| Pages (from-to) | 1-27 |
| Number of pages | 27 |
| Journal | Pacific Journal of Mathematics |
| Volume | 305 |
| Issue number | 1 |
| DOIs | |
| State | Published - Mar 2020 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2020, Mathematical Sciences Publishers.
Keywords
- Dehn surgery
- Poincaré homology sphere
- lens space
- tunnel number
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