Vol. 305, No. 1, 2020

 Recent Issues Vol. 309: 1  2 Vol. 308: 1  2 Vol. 307: 1  2 Vol. 306: 1  2 Vol. 305: 1  2 Vol. 304: 1  2 Vol. 303: 1  2 Vol. 302: 1  2 Online Archive Volume: Issue:
 The Journal Subscriptions Editorial Board Officers Contacts Submission Guidelines Submission Form Policies for Authors ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Special Issues Author Index To Appear Other MSP Journals
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