黎曼曲面讲义

出版时间:2000-12  出版社:世界图书出版公司  作者:Otto Forster  页数:254  
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内容概要

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.

书籍目录

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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用户评论 (总计5条)

 
 

  •   This book grew out of lec***es 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 ***plex manifolds which, in the special case of one ***plex variable, ***n out to be particularly elementary ad transparent.
  •   学黎曼几何入门用这本书就可以,虽然我一直对世界图书出版社影印的这些书的印刷质量不敢恭维
  •   讲得比较详细,题目很多,适合初学者。
  •   我支持GTM的书!
  •   内容难度还是相当大的,不过不难就不叫数学了
 

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