四维流形上的群作用与规范理论

In this project, we study the gauge theory on 4-mainifold with smooth group actionin details. We also discuss the relations between the moduli space of 4-manifolds and the moduli space of quotient 4-manifolds and computer the gauge invariant, i.e. Donaldson invariant and Seiberg-Witten invariant of some 4-manifolds with smooth group actions, in the meantimewe use the results we get to study the differential structures of some.4-manifplds. As an application, we use the equvariant gauge theory especially.Srrberg-Witten theory to study the smooth group action on some 4-manifolds and get some properties about the geometry and topology of some 4-manifold.

系统研究具有光滑群作用的四维流规范理论，特别是讲座其上的模空间与商流形上的模空间之间的关系，并计算出某些具有群作用的四维流形的规范理论的不变量并讨论其微分结构。作为应用，将运用这一理论研究四维流形上的光滑群作用，提示这些四维流形的几何和拓扑的许多内在性质。本项目的研究不仅具有重要的理论意义，还将推动四维流形的研究。