# Handle attaching in symplectic homology and the Chord Conjecture

@article{Cieliebak2002HandleAI,
title={Handle attaching in symplectic homology and the Chord Conjecture},
author={Kai Cieliebak},
journal={Journal of the European Mathematical Society},
year={2002},
volume={4},
pages={115-142}
}
• 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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