### 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 Poincaŕe homology sphere.

Original language | English (US) |
---|---|

Pages (from-to) | 1071-1074 |

Number of pages | 4 |

Journal | Proceedings of the American Mathematical Society |

Volume | 142 |

Issue number | 3 |

DOIs | |

State | Published - 2014 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

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

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 142, no. 3, pp. 1071-1074. https://doi.org/10.1090/S0002-9939-2013-11832-0

}

TY - JOUR

T1 - The Poincaré homology sphere and almost-simple knots in lens spaces

AU - Baker, Kenneth

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84891893960&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84891893960&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2013-11832-0

DO - 10.1090/S0002-9939-2013-11832-0

M3 - Article

AN - SCOPUS:84891893960

VL - 142

SP - 1071

EP - 1074

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -