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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Poincaré homology sphere and almost-simple knots in lens spaces
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by Kenneth L. Baker PDF
Proc. Amer. Math. Soc. 142 (2014), 1071-1074 Request permission


Hedden defined two knots in each lens space that, through analogies with their knot Floer homology and doubly pointed Heegaard diagrams of genus one, may be viewed as generalizations of the two trefoils in $S^3$. Rasmussen showed that when the ‘left-handed’ one is in the homology class of the dual to a Berge knot of type VII, it admits an L-space homology sphere surgery. In this note we give a simple proof that these L-space homology spheres are always the Poincaré homology sphere.
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Additional Information
  • Kenneth L. Baker
  • Affiliation: Department of Mathematics, University of Miami, P.O. Box 249085, Coral Gables, Florida 33124-4250
  • MR Author ID: 794754
  • Email:
  • Received by editor(s): April 18, 2012
  • Published electronically: December 13, 2013
  • Additional Notes: This work was partially supported by grant No. 209184 from the Simons Foundation.
  • Communicated by: Daniel Ruberman
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 142 (2014), 1071-1074
  • MSC (2010): Primary 57M27
  • DOI:
  • MathSciNet review: 3148540