Poincare homology sphere, lens space surgeries, and some knots with tunnel number two
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.
Citation
Baker, K.L., Hoffman, N.R. (2015). The Poincare homology sphere, lens space surgeries, and some knots with tunnel number two.