Lectures on Riemann Surfaces

✍ Scribed by Otto Forster, Bruce Gilligan

• Publisher: Springer-Verlag GmbH
• Year: 1991
• Tongue: English
• Leaves: 257
• Series: Graduate texts in mathematics 81
• Edition: Korr Nachdr. d. 1. A. von 1981
• Category: Library

✦ Synopsis

This book grew out of lectures on Riemann surfaces given by Otto Forster at the Universities of Munich, Regensburg and Munster. It provides an introduction to the subject, as well as presenting methods used in the study of complex manifolds in the special case of complex dimension one. In the first chapter, the author considers Riemann surfaces as covering spaces, develops the pertinent basics of topology and focuses on algebraic functions. The next chapter is devoted to the theory of compact Riemann surfaces and cohomology groups, with the main classical results (including the Riemann-Roch theorem, Abel's theorem and Jacobi's inversion problem). The final section covers the Riemann mapping theorem for simply connected Riemann surfaces, and the main theorems of Behnke-Stein for non-compact Riemann surfaces (the Runge approximation theorem and the theorems of Mittag-Leffler and Weierstrass).