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The Poincaré homology sphere and almost-simple knots in lens spaces


Author: Kenneth L. Baker
Journal: Proc. Amer. Math. Soc. 142 (2014), 1071-1074
MSC (2010): Primary 57M27
Published electronically: December 13, 2013
MathSciNet review: 3148540
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Abstract: 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
Email: k.baker@math.miami.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-11832-0
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
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.