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arXiv · 1712.02948

On tamed almost complex four manifolds

Qiang Tan·Hongyu Wang·Jiuru Zhou·Peng Zhu
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Abstract

This paper proves that on any tamed closed almost complex four-manifold $(M,J)$ whose dimension of $J$-anti-invariant cohomology is equal to the self-dual second Betti number minus one, there exists a new symplectic form compatible with the given almost complex structure $J$. In particular, if the self-dual second Betti number is one, we give an affirmative answer to a question of Donaldson for tamed closed almost complex four-manifolds. Our approach is along the lines used by Buchdahl to give a unified proof of the Kodaira conjecture.

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Qiang Tan, Hongyu Wang, Jiuru Zhou, Peng Zhu. 2019-11-26. On tamed almost complex four manifolds. https://arxiv.org/abs/1712.02948

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