Abstract:We define a class of symplectic manifolds which includes all geometrically bounded symplectic manifolds. In this class we develop a formalism for Floer theory. We show that such a manifold carries a c...We define a class of symplectic manifolds which includes all geometrically bounded symplectic manifolds. In this class we develop a formalism for Floer theory. We show that such a manifold carries a cofinal symplectically invariant set of Floer data which allow the definition of Floer complexes. Moreover, the set of all such Floer complexes forms a directed system. This gives rise to a symplectic invariant we call universal symplectic cohomology. We show that symplectic cohomology as hitherto defined for Liouville domains coincides with universal symplectic cohomology. We discuss applications to the problem of nearby existence of periodic orbits. The results rest on a novel approach to controlling the diameters of Floer trajectories.Read More
Publication Year: 2015
Publication Date: 2015-10-14
Language: en
Type: preprint
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Cited By Count: 14
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