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Lectures on Riemann Surfaces : Graduate Texts in Mathematics - Bruce Gilligan

Lectures on Riemann Surfaces

Graduate Texts in Mathematics

By: Otto Forster, Bruce Gilligan (Translator)

Hardcover

Published: 1st September 1999
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This book grew out of lectures on Riemann surfaces given by Otto Forster at the universities of Munich, Regensburg, and Munster. 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.

O. Forster and B. Gilligan

Lectures on Riemann Surfaces

"A very attractive addition to the list in the form of a well-conceived and handsomely produced textbook based on several years' lecturing experience . . . This book deserves very serious consideration as a text for anyone contemplating giving a course on Riemann surfaces. The reviewer is inclined to think that it may well become a favorite."-MATHEMATICAL REVIEWS

Covering Spaces
Compact Riemann Surfaces
Non-compact Riemann Surfaces
Appendix
References
Symbol
Index
Author and Subject
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387906171
ISBN-10: 0387906177
Series: Graduate Texts in Mathematics : Book 81
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 256
Published: 1st September 1999
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.4 x 15.6  x 1.91
Weight (kg): 0.55