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
- 2. Elementary Properties of Holomorphic Mappings
- 1. The Definition of Riemann Surfaces
- 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
- 13. Dolbeault's Lemma
- 12. Cohomology Groups
- 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
- 23. Countable Topology
- 22. The Dirichlet Boundary Value Problem
- Appendix
- A. Partions of Unity
- B. Topological Vector Spaces
- A. Partions of Unity
O. Forster: Analysis 1 |
O. Forster:
Analysis 2 |
O. Forster:
Analysis 3 |
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Algorithmische Zahlentheorie |
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Otto Forster 2018-06-22