Starting from a suitable set of self-diffeomorphisms of a closed Riemann surface, we present a general branched covering method to construct surface bundles over surfaces with positive signature. Armed with this method, we study the classification problem for both surface bundles with nonzero signature and closed simply connected smooth $\operatorname{spin} 4$-manifolds.

中文翻译：

---

从黎曼曲面的自同构到平滑的$ 4 $流形

从一个封闭的黎曼曲面的一组合适的自微分开始，我们提出了一种通用的分支覆盖方法，以在具有正签名的表面上构造表面束。有了这种方法，我们研究了具有非零特征的表面束和闭合的简单连接的平滑$ \ operatorname {spin} 4 $流形的分类问题。