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Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds. (English) Zbl 1225.53066

Summary: We introduce certain homology and cohomology subgroups for any almost complex structure and study their pureness, fullness and duality properties. Motivated by a question of Donaldson, we use these groups to relate \(J\)-tamed symplectic cones and \(J\)-compatible symplectic cones over a large class of almost complex manifolds, including all Kähler manifolds, almost Kähler 4-manifolds and complex surfaces.

MSC:

53C56 Other complex differential geometry
32Q60 Almost complex manifolds
53C55 Global differential geometry of Hermitian and Kählerian manifolds
55N99 Homology and cohomology theories in algebraic topology
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