Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds

Details Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds

2007-08-19

arxiv.org/abs/0708.2520v4

Mathematics

Symplectic Geometry

v3 substantially revised and title changed, v4 One main result (Theorem 1.3) substantially improved

Scientific paper

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.

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