关于殆复流形的最小贝蒂数和
On the minimal sum of Betti numbers of an almost complex manifold
摘要：
我们表明，只有合理的同源领域，可以承认殆复结构发生在二维和六维。此外，我们还提供了无穷多个六维有理同调球面的例子，这些球面可以有殆复结构，也可以有无穷多个不可以有复结构。证明了如果闭殆复流形的贝蒂数和为3，则它的维数一定是2的幂.
英文摘要：
We show that the only rational homology spheres which can admit almost complex structures occur in dimensions two and six. Moreover, we provide infinitely many examples of six-dimensional rational homology spheres which admit almost complex structures, and infinitely many which do not. We then show that if a closed almost complex manifold has sum of Betti numbers three, then its dimension must be a power of two.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
