#### Vol. 305, No. 1, 2020

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The Poincaré homology sphere, lens space surgeries, and some knots with tunnel number two

### Appendix: Neil R. Hoffman

Vol. 305 (2020), No. 1, 1–27
##### Abstract

We exhibit an infinite family of knots in the Poincaré 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 Poincaré homology sphere with a lens space surgery has either no symmetries or just a single strong involution.

##### Keywords
Poincaré homology sphere, Dehn surgery, lens space, tunnel number
Primary: 57M27