Lectures on Riemann Surfaces

RezensionO. 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

Inhaltsangabe1 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.