| A Note on Donaldson＇s ＂Tamed to Compatible＂, Question |
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| 作者姓名： | TAN QIANG Xu HAI FENG |
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| 作者单位： | School of Mathematics, Yangzhou University, Yangzhou, Jiangsu, 225002 |
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| 基金项目： | The NSF （11071208 and 11126046） of China and the Postgraduate Innovation Project （CXZZ13_0888） of Jiangsu Province. Acknowledgements The authors are very grateful to Professor Wang Hong-yu for his insightful discussions and the reviewers for having pointed out several improvements in writting this paper. |
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| 摘 要： | 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. 7287vl math. SC]. 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.
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A Note on Donaldson's "Tamed to Compatible" Question |
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| TAN QIANG,Xu HAI,FENG.A Note on Donaldson's "Tamed to Compatible" Question[J].Communications in Mathematical Research,2014,30(2):179-182. |
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| Authors: | Qiang Tan & Haifeng Xu |
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| Abstract: | 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. |
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| Keywords: | compact almost complex 4-manifold ω-tame almost complex structure ω-compatible almost complex structure |
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