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1 October 2009 A duality exact sequence for legendrian contact homology
Tobias Ekholm, John B. Etnyre, Joshua M. Sabloff
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Duke Math. J. 150(1): 1-75 (1 October 2009). DOI: 10.1215/00127094-2009-046


We establish a long exact sequence for Legendrian submanifolds LP×R, where P is an exact symplectic manifold, which admit a Hamiltonian isotopy that displaces the projection of L to P off of itself. In this sequence, the singular homology H* maps to linearized contact cohomology CH*, which maps to linearized contact homology CH*, which maps to singular homology. In particular, the sequence implies a duality between Ker(CH*H*) and CH*/Im(H*). Furthermore, this duality is compatible with Poincaré duality in L in the following sense: the Poincaré dual of a singular class which is the image of aCH* maps to a class αCH* such that α(a)=1.

The exact sequence generalizes the duality for Legendrian knots in R3 (see [26]) and leads to a refinement of the Arnold conjecture for double points of an exact Lagrangian admitting a Legendrian lift with linearizable contact homology, first proved in [7]


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Tobias Ekholm. John B. Etnyre. Joshua M. Sabloff. "A duality exact sequence for legendrian contact homology." Duke Math. J. 150 (1) 1 - 75, 1 October 2009.


Published: 1 October 2009
First available in Project Euclid: 15 September 2009

zbMATH: 1193.53179
MathSciNet: MR2560107
Digital Object Identifier: 10.1215/00127094-2009-046

Primary: 53D35
Secondary: 57R17

Rights: Copyright © 2009 Duke University Press


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Vol.150 • No. 1 • 1 October 2009
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