The Poincare homology sphere and almost simple knots in lens spaces

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 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 Poincaré homology sphere.

arXiv comment3 pages, 4 figures

References in corpus (3)

• Lens space surgeries and L-space homology spheres
• Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
• The lens space realization problem