Holomorphic triangles and invariants for smooth four-manifolds

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In earlier articles, the authors introduced invariants for closed, oriented three-manifolds, defined using a variant of Lagrangian Floer homology in the symmetric products of Riemann surfaces. The aim of this article is to introduce invariants of oriented, smooth four-manifolds, built using these Floer homology groups. This four-dimensional theory also endows the corresponding three-dimensional theories with additional structure: an absolute grading of certain of its Floer homology groups.

Original languageEnglish (US)
Pages (from-to)326-400
Number of pages75
JournalAdvances in Mathematics
Issue number2
StatePublished - Jun 1 2006

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Floer homology
  • Four-manifolds


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