Description
Springer Lectures on Riemann Surfaces by Otto Forster, Bruce Gilligan
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._x000D__x000D__x000D_From the reviews: "This book deserves very serious consideration as a text for anyone contemplating giving a course on Riemann surfaces."--MATHEMATICAL REVIEWS_x000D_ Table of contents :- _x000D_
1 Covering Spaces.- 1. The Definition of Riemann Surfaces.- 2. Elementary Properties of Holomorphic Mappings.- 3. Homotopy of Curves. The Fundamental Group.- 4. Branched and Unbranched Coverings.- 5. The Universal Covering and Covering Transformations.- 6. Sheaves.- 7. Analytic Continuation.- 8. Algebraic Functions.- 9. Differential Forms.- 10. The Integration of Differential Forms.- 11. Linear Differential Equations.- 2 Compact Riemann Surfaces.- 12. Cohomology Groups.- 13. Dolbeault's Lemma.- 14. A Finiteness Theorem.- 15. The Exact Cohomology Sequence.- 16. The Riemann-Roch Theorem.- 17. The Serre Duality Theorem.- 18. Functions and Differential Forms with Prescribed Principal Parts.- 19. Harmonic Differential Forms.- 20. Abel's Theorem.- 21. The Jacobi Inversion Problem.- 3 Non-compact Riemann Surfaces.- 22. The Dirichlet Boundary Value Problem.- 23. Countable Topology.- 24. Weyl's Lemma.- 25. The Runge Approximation Theorem.- 26. The Theorems of Mittag-Leffler and Weierstrass.- 27. The Riemann Mapping Theorem.- 28. Functions with Prescribed Summands of Automorphy.- 29. Line and Vector Bundles.- 30. The Triviality of Vector Bundles.- 31. The Riemann-Hilbert Problem.- A. Partitions of Unity.- B. Topological Vector Spaces.- References.- Symbol Index.- Author and Subject Index._x000D_