Handle attaching in symplectic homology and the Chord Conjecture |
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Authors: | Kai Cieliebak |
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Institution: | (1) Stanford University, Department of Mathematics, Stanford, CA 94305–2125, USA, US |
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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.?The proof relies
on the behaviour of symplectic homology under handle attaching. The main observation is that symplectic homology only changes
in the presence of chords.
Received July 14, 2000 / final version received June 1, 2001?Published online August 1, 2001 |
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Keywords: | Mathematics Subject Classification (2000): 53D 57R 58C |
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