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

Baker, Kenneth

doi:10.1090/S0002-9939-2013-11832-0

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

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.

References

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