Otto Forster: Lectures on Riemann Surfaces

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

Other books by O. Forster

Otto Forster (), 1999-08-20