书籍详情
黎曼曲面讲义
作者：（德）Otto Forster著；（加）Bruce Gilligan译
出版社：世界图书出版公司北京公司
出版时间：2003-07-01
ISBN：9787506201117
定价：¥39.00
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内容简介
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.本书为英文版！
作者简介
暂缺《黎曼曲面讲义》作者简介
目录
Preface
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. Partitions of Unity
B. Topological Vector Spaces
References
Symbol Index
Author and Subject Index
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. Partitions of Unity
B. Topological Vector Spaces
References
Symbol Index
Author and Subject Index
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