A geometric proof of the Fintushel-Stern formula1

Olivier Collin; Nikolai Saveliev

doi:10.1006/aima.1999.1842

A geometric proof of the Fintushel-Stern formula¹

Olivier Collin, Nikolai Saveliev

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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
DOIs	https://doi.org/10.1006/aima.1999.1842
State	Published - Nov 10 1999
Externally published	Yes

Keywords

Casson invariant
Knot signatures
Milnor fiber

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1006/aima.1999.1842

Cite this

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title = "A geometric proof of the Fintushel-Stern formula1",

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.",

keywords = "Casson invariant, Knot signatures, Milnor fiber",

author = "Olivier Collin and Nikolai Saveliev",

note = "Funding Information: 1The first author is supported by an NSERC Post-doctoral Fellowship. The work of the second author was partially supported by NSF Grant DMS 9704204. The first author thanks the Mathematics Department of Yale University for their hospitality and Ronnie Lee for discussions about the work done in [3]. The second author thanks Frank Raymond for helpful conversations and sharing his expertise.",

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AU - Saveliev, Nikolai

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PY - 1999/11/10

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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.

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KW - Casson invariant

KW - Knot signatures

KW - Milnor fiber

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