Author | Forster, Otto. author |
---|---|
Title | Lectures on Riemann Surfaces [electronic resource] / by Otto Forster |
Imprint | New York, NY : Springer New York, 1981 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5961-9 |
Descript | VIII, 256 p. online resource |
1 Covering Spaces -- ยง1. The Definition of Riemann Surfaces -- ยง2. Elementary Properties of Holomorphic Mappings -- ยง3. Homotopy of Curves. The Fundamental Group -- ยง4. Branched and Unbranched Coverings -- ยง5. The Universal Covering and Covering Transformations -- ยง6. Sheaves -- ยง7. Analytic Continuation -- ยง8. Algebraic Functions -- ยง9. Differential Forms -- ยง10. The Integration of Differential Forms -- ยง11. Linear Differential Equations -- 2 Compact Riemann Surfaces -- ยง12. Cohomology Groups -- ยง13. Dolbeaultโs Lemma -- ยง14. A Finiteness Theorem -- ยง15. The Exact Cohomology Sequence -- ยง16. The Riemann-Roch Theorem -- ยง17. The Serre Duality Theorem -- ยง18. Functions and Differential Forms with Prescribed Principal Parts -- ยง19. Harmonic Differential Forms -- ยง20. Abelโs Theorem -- ยง21. The Jacobi Inversion Problem -- 3 Non-compact Riemann Surfaces -- ยง22. The Dirichlet Boundary Value Problem -- ยง23. Countable Topology -- ยง24. Weylโs Lemma -- ยง25. The Runge Approximation Theorem -- ยง26. The Theorems of Mittag-Leffler and Weierstrass -- ยง27. The Riemann Mapping Theorem -- ยง28. Functions with Prescribed Summands of Automorphy -- ยง29. Line and Vector Bundles -- ยง30. The Triviality of Vector Bundles -- ยง31. The Riemann-Hilbert Problem -- A. Partitions of Unity -- B. Topological Vector Spaces -- References -- Symbol Index -- Author and Subject Index