Commun. Math. Res., 30 (2014), pp. 179-182.
Published online: 2021-05
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Recently, Tedi Draghici and Weiyi Zhang studied Donaldson's "tamed to compatible" question (Draghici T, Zhang W. A note on exact forms on almost complex manifolds. arXiv: 1111. 7287v1 [math. SG]. Submitted on 30 Nov. 2011). That is, for a compact almost complex 4-manifold whose almost complex structure is tamed by a symplectic form, is there a symplectic form compatible with this almost complex structure? They got several equivalent forms of this problem by studying the space of exact forms on such a manifold. With these equivalent forms, they proved a result which can be thought as a further partial answer to Donaldson's question in dimension 4. In this note, we give another simpler proof of their result.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2014.02.08}, url = {http://global-sci.org/intro/article_detail/cmr/18980.html} }Recently, Tedi Draghici and Weiyi Zhang studied Donaldson's "tamed to compatible" question (Draghici T, Zhang W. A note on exact forms on almost complex manifolds. arXiv: 1111. 7287v1 [math. SG]. Submitted on 30 Nov. 2011). That is, for a compact almost complex 4-manifold whose almost complex structure is tamed by a symplectic form, is there a symplectic form compatible with this almost complex structure? They got several equivalent forms of this problem by studying the space of exact forms on such a manifold. With these equivalent forms, they proved a result which can be thought as a further partial answer to Donaldson's question in dimension 4. In this note, we give another simpler proof of their result.