The Poincare homology sphere and almost simple knots in lens spaces

Details The Poincare homology sphere and almost simple knots in lens spaces The Poincare homology sphere and almost simple knots in lens spaces

2011-11-29

arxiv.org/abs/1111.6877v1

Mathematics

Geometric Topology

3 pages, 4 figures

Scientific paper

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 shows 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 Poincar\'e homology sphere.

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