Topological studies on the surface embedded on 4-dimensional manifolds and their deformations

为了进一步完善对嵌入在4流形中的封闭曲面的变形和映射类群的研究，我们从拓扑学的角度对映射类群进行了一些研究。特别地，我们得到了大周期周期映射的唯一性、嵌入3球的有界曲面的正则同伦变形、三维把手体映射类群的Nielsen实现问题，以及标准嵌入4球的不可定向封闭曲面的映射类群的Nielsen实现问题。

In order to improve the study on deformations and the mapping class groups of closed surfaces embedded in 4-manifolds, we made several researches on the mapping class group from the topological viewpoint. Especially, we obtained results on the uniqueness of periodic maps with large periods, the regular homotopic deformations of the bounded surface embedded in the 3-sphere, the Nielsen realization problems on the mapping class groups of the 3-dimensional handlebodies, and the mapping class groups of the nonorientable closed surfaces standardly embedded in the 4-sphere.