Handle attaching in symplectic homology and the Chord Conjecture

  title={Handle attaching in symplectic homology and the Chord Conjecture},
  author={Kai Cieliebak},
  journal={Journal of the European Mathematical Society},
  • K. Cieliebak
  • Published 30 June 2002
  • Mathematics
  • Journal of the European Mathematical Society
Abstract.Arnold conjectured that every Legendrian knot in the standard contact structure on the 3-sphere possesses a characteristic chord with respect to any contact form. I confirm this conjecture if the know has Thurston-Bennequin invariant −1. More generally, existence of chords is proved for a standard Legendrian unknot on the boundary of a subcritical Stein manifold of any dimension. There is also a multiplicity result which implies in some situations existence of infinitely many chords… 
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