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Functors and computations in Floer homology with applications. I. (English) Zbl 0954.57015
Floer cohomology of manifolds with contact type boundary is studied. The author constructs two mappings in Floer cohomology where one of them is a map from the Floer cohomology of a manifold \(M\) to the relative cohomology of \(M\) modulo its boundary and the other is associated to a codimension zero embedding. The functorial properties of these two mappings are proved. These maps are also used to define some properties of symplectic manifolds with contact type boundary which are algebraic versions of the Weinstein conjecture, asserting existence of closed characteristics on \(\partial M\). It is also proved that the above property implies some restrictions on Lagrangian embeddings, and also yields in certain cases existence results for holomorphic curves bounded by the Lagrange submanifolds.

MSC:
57R58 Floer homology
53D99 Symplectic geometry, contact geometry
57R17 Symplectic and contact topology in high or arbitrary dimension
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