万有Teichmller空间的某些性质

Some properties of universal Teichmüller space

本文讨论了以单位国内共形映射的对数导数为模型的万有Teichm(?)ller空间的拓扑性质,用较I. V. Zhuravlev简单的方法证明这种万有Teichm(?)ller空间的不连通性并得到更深入的结果,证明其每个连通分支是可缩的。

In this note,we discuss the topology of a model of the universal Teichmuller space T1. I. V. Zhuralev proved that T1 is disconnected. We study the space further and prove that every component of T1 is contractible. Using a different method, We give a simpter proof of the dis-connectivity of T1.