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A duality exact sequence for legendrian contact homology
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Geometry and Logic.
Department of mathematics, Georgia Tech.
Department of mathematics, Haverford College.
2009 (English)In: Duke mathematical journal, ISSN 0012-7094, Vol. 150, no 1, 1-75 p.Article in journal (Refereed) Published
Abstract [en]

We establish a long exact sequence for Legendrian submanifolds L⊂P×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 a∈CH* maps to a class α∈CH* 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]

Place, publisher, year, edition, pages
Duke University Press , 2009. Vol. 150, no 1, 1-75 p.
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URN: urn:nbn:se:uu:diva-109001DOI: 10.1215/00127094-2009-046ISI: 000270581600001OAI: oai:DiVA.org:uu-109001DiVA: diva2:242092
Available from: 2009-10-06 Created: 2009-10-06 Last updated: 2010-07-02Bibliographically approved

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