Floer homology of brieskorn homology spheres

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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 μ¯invariant of W. Neumann and L. Siebenmann for Seifert fibered homology spheres, and investigate its behavior with respect.

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

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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