Lectures on Reimann Surfaces

ISBN-10: 0387906177

ISBN-13: 9780387906171

Edition: 1981 (Reprint)

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Description: This book grew out of lectures on Riemann surfaces given by Otto Forster at the universities of Munich, Regensburg, and Mnster. It provides a concise modern introduction to this rewarding subject, as well as presenting methods used in the study of complex manifolds in the special case of complex dimension one. The material corresponds roughly to three semesters of lectures, arranged in a flexible sequence involving a minimum of prerequisites. 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). The value of this translation is enhanced by newly prepared exercises.

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Book details

List price: $89.95
Copyright year: 1981
Publisher: Springer
Publication date: 8/13/1999
Binding: Hardcover
Pages: 256
Size: 6.14" wide x 9.21" long x 0.75" tall
Weight: 2.684
Language: English

Covering Spaces
Compact Riemann Surfaces
Non-compact Riemann Surfaces
Appendix
References
Symbol
Index
Author and Subject
Index
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