4-MANIFOLDS AND RIEMANN SURFACES

黎曼曲面是具有复杂结构的闭曲面。黎曼曲面的同构类构成了一个称为模空间的复轨道。它可以通过添加某些“边界”来压缩。本文的主要成果是在紧化模空间上成功地构造了一个“泛退化黎曼曲面族”。目前正在准备一篇论文，但其结果有望应用于黎曼曲面纤维化的4-流形的许多问题。

A Riemann surface is a closed surface carrying a complex structure. The isomorphism classes of Riemann surfaces make a complex orbifold called the moduli space. It can be compactified by adding certain "boundaries". The main achievement is that we have succeeded in constructing a "universal degenerating family of Riemann surfaces" over the compactified moduli space. A paper is now in preparation, but the result is expected to be applied in many problems of 4-manifolds which are fibered by Riemann surfaces.