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

Research output: Contribution to journalArticle

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 S3. 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 Poincaŕe homology sphere.

Original languageEnglish (US)
Pages (from-to)1071-1074
Number of pages4
JournalProceedings of the American Mathematical Society
Volume142
Issue number3
DOIs
StatePublished - 2014

Fingerprint

Homology Spheres
Lens Space
Knot
Lenses
L-space
Heegaard Diagram
Trefoil
Floer Homology
Left handed
Surgery
Analogy
Homology
Genus

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

The Poincaré homology sphere and almost-simple knots in lens spaces. / Baker, Kenneth.

In: Proceedings of the American Mathematical Society, Vol. 142, No. 3, 2014, p. 1071-1074.

Research output: Contribution to journalArticle

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