Heegaard Floer invariants of Legendrian knots in contact three-manifolds

Paolo Lisca, Peter Ozsváth, András I. Stipsicz, Zoltán Szabó

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38 Citations (Scopus)

Abstract

We define invariants of null-homologous Legendrian and transverse knots in contact 3-manifolds. The invariants are determined by elements of the knot Floer homology of the underlying smooth knot. We compute these invariants, and show that they do not vanish for certain non-loose knots in overtwisted 3-spheres. Moreover, we apply the invariants to find transversely non-simple knot types in many overtwisted contact 3-manifolds.

Original languageEnglish
Pages (from-to)1307-1363
Number of pages57
JournalJournal of the European Mathematical Society
Volume11
Issue number6
Publication statusPublished - Dec 1 2009

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Keywords

  • Heegaard Floer homology
  • Legendrian knots
  • Transverse knots

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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