A note on exact forms on almost complex manifolds

Details A note on exact forms on almost complex manifolds A note on exact forms on almost complex manifolds

2011-11-30

arxiv.org/abs/1111.7287v1

Mathematics

Symplectic Geometry

7 pages

Scientific paper

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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