Communications in Analysis and Geometry
Volume 17 (2009)
Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds
Pages: 651 – 683
We introduce certain homology and cohomology subgroups for anyalmost complex structure and study their pureness, fullness andduality properties. Motivated by a question of Donaldson, we usethese groups to relate $J$-tamed symplectic cones and$J$-compatible symplectic cones over a large class of almostcomplex manifolds, including all Kähler manifolds, almostKähler $4$-manifolds and complex surfaces.