标题： 关于模空间和Teichm{ü}ller空间的早期历史 显示英文标题

标题： On the early history of moduli and Teichm{ü}ller spaces

摘要： 我们综述了对黎曼模空间和克莱因曲面空间的一些主要贡献。 我们的报告具有历史性质，但重点在于数学思想的链条。 我们从黎曼曲面的介绍开始，最后以发现黎曼模空间和克莱因曲面空间的一些基本结构结束。 我们指出了几个似乎许多代数几何学家和分析学家在该理论中并不了解的事实。 我们感兴趣的时间段始于1851年黎曼的时代，结束于20世纪60年代初，当时Ahlfors和Bers确认了克莱因的结果是正确的。 本文是为《Lipman Bers, a life in Mathematics》一书撰写的，由Linda Keen、Irwin Kra和Rubi Rodriguez编辑（美国数学学会，2015年）。 本文献给Lipman Bers的回忆，他首先是一位复分析学家，并将大部分生命和精力投入到克莱因曲面空间的分析结构上。 然而，他的分析工作与几何学和拓扑学密不可分。 在这篇综述中，我们强调了这项工作与黎曼、庞加莱、克莱因、布劳威尔、西格尔、克莱因、魏尔、格罗滕迪克等人的工作的关系和逻辑依赖性。 我们解释了这些想法背后的动机。 在此过程中，我们指出了几个似乎许多克莱因理论家并不了解的事实。 显示英文摘要

摘要： We survey some major contributions to Riemann's moduli space and Teichm{\"u}ller space. Our report has a historical character, but the stress is on the chain of mathematical ideas. We start with the introduction of Riemann surfaces, and we end with the discovery of some of the basic structures of Riemann's moduli space and Teichm{\"u}ller space. We point out several facts which seem to be unknown to many algebraic geometers and analysts working in the theory. The period we are interested in starts with Riemann, in 1851, and ends in the early 1960s, when Ahlfors and Bers confirmed that Teichm{\"u}ller's results were correct.This paper was written for the book "Lipman Bers, a life in Mathematics," edited by Linda Keen , Irwin Kra and Rubi Rodriguez (Amercian Mathematical Society, 2015). It is dedicated to the memory of Lipman Bers who was above all a complex analyst and spent a large part of his life and energy working on the analytic structure of Teichm{\"u}ller space. His work on analysis is nevertheless inseparable from geometry and topology. In this survey, we highlight the relations and the logical dependence between this work and the works of Riemann, Poincar{\'e}, Klein, Brouwer, Siegel, Teichm{\"u}ller, Weil, Grothendieck and others. We explain the motivation behind the ideas. In doing so, we point out several facts which seem to be unknown to many Teichm{\"u}ller theorists.