A note on exact forms on almost complex manifolds

  title={A note on exact forms on almost complex manifolds},
  author={T. Drăghici and W. Zhang},
  journal={arXiv: Symplectic Geometry},
  • T. Drăghici, W. Zhang
  • Published 2011
  • Mathematics
  • arXiv: Symplectic Geometry
  • Reformulations of Donaldson's "tamed to compatible" question are obtained in terms of spaces of exact forms on a compact almost complex manifold $(M^{2n},J)$. In dimension 4, we show that $J$ admits a compatible symplectic form if and only if $J$ admits tamed symplectic forms with arbitrarily given $J$-anti-invariant parts. Some observations about the cohomology of $J$-modified de Rham complexes are also made. 
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