### Abstract

Every Brieskorn homology sphere Σ(p, q, r) is a double cover of the 3-sphere ramified over a Montesinos knot k(p, q, r). We express the Floer homology of Σ(p, q, r) in terms of certain invariants of the knot k(p, q, r), among which are the knot signature and the Jones polynomial. We also define an integer valued invariant of integral homology 3-spheres which agrees with the μ̄-invariant of W. Neumann and L. Siebenmann for Seifert fibered homology spheres, and investigate its behavior with respect to homology 4-cobordism.

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

Pages (from-to) | 15-87 |

Number of pages | 73 |

Journal | Journal of Differential Geometry |

Volume | 53 |

Issue number | 1 |

State | Published - Sep 1999 |

Externally published | Yes |

### Fingerprint

### Keywords

- Casson invariant
- Floer homology
- Homology cobordism
- Jones polynomial
- Knot signature
- Montesinos knots
- Seifert manifolds

### ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis
- Geometry and Topology

### Cite this

*Journal of Differential Geometry*,

*53*(1), 15-87.

**Floer homology of Brieskorn homology spheres.** / Saveliev, Nikolai.

Research output: Contribution to journal › Article

*Journal of Differential Geometry*, vol. 53, no. 1, pp. 15-87.

}

TY - JOUR

T1 - Floer homology of Brieskorn homology spheres

AU - Saveliev, Nikolai

PY - 1999/9

Y1 - 1999/9

N2 - Every Brieskorn homology sphere Σ(p, q, r) is a double cover of the 3-sphere ramified over a Montesinos knot k(p, q, r). We express the Floer homology of Σ(p, q, r) in terms of certain invariants of the knot k(p, q, r), among which are the knot signature and the Jones polynomial. We also define an integer valued invariant of integral homology 3-spheres which agrees with the μ̄-invariant of W. Neumann and L. Siebenmann for Seifert fibered homology spheres, and investigate its behavior with respect to homology 4-cobordism.

AB - Every Brieskorn homology sphere Σ(p, q, r) is a double cover of the 3-sphere ramified over a Montesinos knot k(p, q, r). We express the Floer homology of Σ(p, q, r) in terms of certain invariants of the knot k(p, q, r), among which are the knot signature and the Jones polynomial. We also define an integer valued invariant of integral homology 3-spheres which agrees with the μ̄-invariant of W. Neumann and L. Siebenmann for Seifert fibered homology spheres, and investigate its behavior with respect to homology 4-cobordism.

KW - Casson invariant

KW - Floer homology

KW - Homology cobordism

KW - Jones polynomial

KW - Knot signature

KW - Montesinos knots

KW - Seifert manifolds

UR - http://www.scopus.com/inward/record.url?scp=0002521843&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002521843&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0002521843

VL - 53

SP - 15

EP - 87

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

SN - 0022-040X

IS - 1

ER -