We give necessary and sufficient conditions for a 4-manifold to be a branched covering of $\mathbb{C}{\mathrm{P}}^2$, $S^2\times S^2$, $S^2\stackrel{\sim }{\times }{S}^2$ or $S^3\times S^1$, which are expressed in terms of the Betti numbers and the signature of the 4-manifold. Moreover, we extend these results to include branched coverings of connected sums of the above manifolds. This leads to some new examples of closed simply connected quasiregularly elliptic 4-manifolds.

中文翻译：

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CP2 和其他基本 4 流形的分支覆盖物

我们给出了一个 4-流形是一个分支覆盖的充要条件 $\mathbb{C}{\mathrm{磷}}^2$, ${秒}^2\times {秒}^2$, ${秒}^2\stackrel{～}{\times }{秒}^2$ 或者 ${秒}^3\times {秒}^1$，用 Betti 数和 4 流形的签名表示。此外，我们将这些结果扩展到包括上述流形的连接和的分支覆盖。这导致了一些封闭的简单连接的拟正则椭圆 4 流形的新例子。