Floer homology of Brieskorn homology spheres

Research output: Contribution to journalArticle

11 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)15-87
Number of pages73
JournalJournal of Differential Geometry
Volume53
Issue number1
StatePublished - Sep 1999
Externally publishedYes

Fingerprint

Homology Spheres
Floer Homology
Knot
Invariant
Homology
Jones Polynomial
Cobordism
Signature
Express
Cover
Integer

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

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

In: Journal of Differential Geometry, Vol. 53, No. 1, 09.1999, p. 15-87.

Research output: Contribution to journalArticle

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