黎曼曲面講義

內(nèi)容概要

This book grew out of lectures on Riemann surfaces which the author gave at the universities of Munich, Regensburg and Munster. Its aim is to give an introduction to this rich and beautiful subject, while presenting methods from the theory of complex manifolds which, in the special case of one complex variable, turn out to be particularly elementary ad transparent.

書籍目錄

PrefaceChapter 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 EquationsChapter 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 ProblemChapter 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 ProblemAppendix　A. Partitions of Unity　B. Topological Vector SpacesReferencesSymbol IndexAuthor and Subject Index

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