On non-pure forms on almost complex manifolds

In 2009 T.-J. Li and W. Zhang defined an almost complex structure J on a manifold X to be C^\infty-pure-and-full if the second de Rham cohomology group can be decomposed as a direct sum of the subgroups whose elements are cohomology classes admitting J-invariant and J-anti-invariant representatives. It turns out (see T. Draghici, T.-J. Li and W. Zhang (2010)) that any almost complex structure on a 4-dimensional compact manifold is C^\infty-pure-and-full. We study the J-invariant and J-anti-invariant cohomology subgroups on almost complex manifolds, possibly non-compact. In particular, we prove an analytic continuation result for anti-invariant forms on almost complex manifolds. - See more at: http://www.ams.org/journals/proc/2014-142-11/S0002-9939-2014-11578-4/#sthash.yZn8gAfE.dpuf