### Abstract

The Fintushel-Stern formula asserts that the Casson invariant of a Brieskorn homology sphere Σ(p, q, r) equals 1/8 the signature of its Milnor fiber. We give a geometric proof of this formula, as opposite to computational methods used in the original proof. The formula is also refined to relate equivariant Casson invariants to equivariant signatures.

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

Pages (from-to) | 304-314 |

Number of pages | 11 |

Journal | Advances in Mathematics |

Volume | 147 |

Issue number | 2 |

State | Published - Nov 10 1999 |

Externally published | Yes |

### Fingerprint

### Keywords

- Casson invariant
- Knot signatures
- Milnor fiber

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

^{1}

*Advances in Mathematics*,

*147*(2), 304-314.

**A geometric proof of the Fintushel-Stern formula ^{1} .** / Collin, Olivier; Saveliev, Nikolai.

Research output: Contribution to journal › Article

^{1}',

*Advances in Mathematics*, vol. 147, no. 2, pp. 304-314.

^{1}Advances in Mathematics. 1999 Nov 10;147(2):304-314.

}

TY - JOUR

T1 - A geometric proof of the Fintushel-Stern formula1

AU - Collin, Olivier

AU - Saveliev, Nikolai

PY - 1999/11/10

Y1 - 1999/11/10

N2 - The Fintushel-Stern formula asserts that the Casson invariant of a Brieskorn homology sphere Σ(p, q, r) equals 1/8 the signature of its Milnor fiber. We give a geometric proof of this formula, as opposite to computational methods used in the original proof. The formula is also refined to relate equivariant Casson invariants to equivariant signatures.

AB - The Fintushel-Stern formula asserts that the Casson invariant of a Brieskorn homology sphere Σ(p, q, r) equals 1/8 the signature of its Milnor fiber. We give a geometric proof of this formula, as opposite to computational methods used in the original proof. The formula is also refined to relate equivariant Casson invariants to equivariant signatures.

KW - Casson invariant

KW - Knot signatures

KW - Milnor fiber

UR - http://www.scopus.com/inward/record.url?scp=0033544190&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033544190&partnerID=8YFLogxK

M3 - Article

VL - 147

SP - 304

EP - 314

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 2

ER -