Heegaard Floer homology and contact structures

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Given a contact structure on a closed, oriented three-manifold Y, we describe an invariant that takes values in the three-manifold's Floer homology HF. This invariant vanishes for overtwisted contact structures and is nonzero for Stein-fillable ones. The construction uses Giroux's interpretation of contact structures in terms of open-book decompositions.

Original languageEnglish (US)
Pages (from-to)39-61
Number of pages23
JournalDuke Mathematical Journal
Issue number1
StatePublished - Jul 15 2005

All Science Journal Classification (ASJC) codes

  • General Mathematics


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