Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds
arXiv:0708.2520
Abstract
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 Kahler manifolds, almost Kahler 4-manifolds and complex surfaces.
v3 substantially revised and title changed, v4 One main result (Theorem 1.3) substantially improved