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

Kenneth L. Baker; Neil R. Hoffman

doi:10.2140/pjm.2020.305.1

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arXiv · 1504.06682

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

Kenneth L. Baker·Neil R. Hoffman

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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. In the appendix, it is shown that hyperbolic knots in the Poincare homology sphere with a lens space surgery has either no symmetries or just a single strong involution.

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BibTeX RIS

Kenneth L. Baker, Neil R. Hoffman. 2015-04-25. The Poincare homology sphere, lens space surgeries, and some knots with tunnel number two. https://doi.org/10.2140/pjm.2020.305.1

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