Surface de Riemann

Abstract

In this work, we have undertaken a rigorous study of Riemann surfaces as a fundamental point of convergence between topology, complex analysis, and geometry. We have delved into a key pillar of this rich mathematical structure, starting from topological foundations and extending to the study of its global properties through meromorphic functions. Although this approach is primarily theoretical, it opens up broad perspectives, particularly in exploring the physical and geometric applications of Riemann surfaces. This work illustrates the depth and unity of modern mathematics and attests to the conceptual beauty of the strong connections between analysis, geometry, and algebra