O. Forster: Bücher/Books
Otto Forster: Lectures on Riemann Surfaces
Graduate Texts in Mathematics 81
4th corrected printing
Springer-Verlag 1999
ISBN 0-387-90617-0
Contents
Chapter 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
Chapter 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
Chapter 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
Appendix
A. Partions of Unity
B. Topological Vector Spaces
| O. Forster: Analysis 1 |
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O. Forster:
Analysis 2 |
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O. Forster:
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O. Forster:
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Otto Forster 2018-06-22