A note on exact forms on almost complex manifolds

2011/11/30 by Tedi Draghici, Weiyi Zhang, Draghici, Tedi +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DG #math.SG

paper · pdf · doi:10.48550/arxiv.1111.7287

7 pages

arxiv created 2011/11/30 · arxiv updated 2011/12/01

Abstract

Reformulations of Donaldson's "tamed to compatible" question are obtained in terms of spaces of exact forms on a compact almost complex manifold (M²ⁿ,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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