Department Mathematik



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


  • 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
O. Forster: Analysis 2
O. Forster: Analysis 3
O. Forster: Algorithmische Zahlentheorie
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Otto Forster 2018-06-22