ENGLISH

Lectures on Riemann Surfaces

By Otto Forster

Book information

Publisher
Springer
Year
1991
ISBN
3540906177, 9783540906179
Language
english
Format
DJVU
Filesize
3 MB (3261423 bytes)
Series
Graduate Texts in Mathematics
Pages
262\131
Time added
2011-06-04 13:46:07

Description

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).

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