On the early history of moduli and Teichm{\"u}ller spaces
Norbert A'Campo, Lizhen Ji, Athanase Papadopoulos (IRMA)

TL;DR
This paper surveys the historical development of Riemann's moduli space and Teichmüller space from 1851 to the 1960s, emphasizing the evolution of key ideas and structures in complex analysis, geometry, and topology.
Contribution
It provides a comprehensive historical overview highlighting the logical progression and connections between foundational works in the theory of moduli and Teichmüller spaces.
Findings
Clarifies the historical development of Teichmüller theory.
Highlights overlooked facts relevant to algebraic geometers and analysts.
Connects the works of Riemann, Poincaré, Klein, and others in the evolution of the field.
Abstract
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…
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Taxonomy
TopicsHistory and Theory of Mathematics · Homotopy and Cohomology in Algebraic Topology
