On Tamed Almost Four-Manifolds
On Tamed Almost Four-Manifolds
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论驯服的几乎四流形
DOI：
10.1007/s42543-021-00045-7
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发表时间：
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通讯作者：
Zhu Peng
中科院分区：
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作者：
Tan Qiang;Hongyu Wang;Zhou Jiuru;Zhu Peng
本文证明，在任何驯服的闭几乎复数四流形（M，J）上，其J-反不变上同调维数等于自对偶第二贝蒂数减1，存在与给定的几乎复数结构J相容的新辛形式。特别是，如果自对偶第二贝蒂数为一，我们对唐纳森关于驯服闭几乎复杂四流形的问题给出肯定的答案。我们的方法遵循布赫达尔用来统一证明小平猜想的思路。
This paper proves that on any tamed closed almost complex four-manifold (M,J) whose dimension ofJ-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 structureJ. 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.