A duality exact sequence for legendrian contact homology
2009 (English)In: Duke mathematical journal, ISSN 0012-7094, Vol. 150, no 1, 1-75 p.Article in journal (Refereed) Published
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 ) 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 
Place, publisher, year, edition, pages
Duke University Press , 2009. Vol. 150, no 1, 1-75 p.
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-109001DOI: 10.1215/00127094-2009-046ISI: 000270581600001OAI: oai:DiVA.org:uu-109001DiVA: diva2:242092