广义微分几何讲义

图书信息

图书特色

本书是国际上Diffeology研究领军人物Patrick Iglesias-Zemmour所撰写的讲义，是已出版的Diffeology领域名著《广义微分几何》的配套教学笔记。 本书是国际上Diffeology研究领军人物Patrick Iglesias-Zemmour所撰写的讲义，是已出版的Diffeology领域名著《广义微分几何》的配套教学笔记。

内容简介

《广义微分几何讲义》是已出版的《广义微分几何》（广义微分几何领域**本教材）的配套教学笔记，一半源自作者在汕头大学的授课经历，一半则是作者在同各方学者多年研究探讨后的研究成果、思考、练习等作者希望与读者分享的笔记。全书以时间线为轴，讲述广义微分几何领域的起源和发展，编排合理，每章篇头都有总述、定义、理论等讲解，辅以推论过程，由简到难，自然过渡到结论，很符合授课讲义的风格，其后还有习题、问题、思考探讨等用以巩固讲义知识，并启发思考，对研究微分几何或数学物理的学生与研究人员极为有用。

目录

1. Preface
2. At the Beginning
3. Diffeology, the Axiomatic
4. The Irrational Tori 8
5. Generating Families, Dimension
6. Cartan-De-Rham Calculus
7. Diffeology Fiber Bundles
8. Homotopy Theory in Diffeology
9. Local Diffeology, Modeling
10. Modeling: Manifolds, Orbifolds and Quasifolds
11. Symplectic Mechanics and Diffeology
12. Diffeology and Non-Commutative Geometry
13. Functional Diffeology on Fourier Coefffcients
14. Smooth Function on Periodic Functions
15. Symplectic Diffeology on Smooth Periodic Functions
16. Infinite Torus Action on Smooth Periodic Functions
17. Basic 1-Forms on Principal Fiber Bundles
18. Differential of Holonomy for Torus Bundles
19. Non-symplectic manifold with injective univ. moment map
20. On Riemannian Metric in Diffeology
21. A Few Half-Lines
22. 1-Forms on Half-Lines
23. 1-Forms on the Subset Half-Line
24. Cotangent Space of the Half-Line
25. 1-Forms on Half-Spaces
26. p-Forms on Half-Spaces
27. p-Forms on Corners
28. Differential Forms on the Cross
29. A note on Hamiltonian Diffeomorphisms
30. Differential of a Lie-Group Valued Function
31. The Geodesics of the 2-Torus
32. The Use of the Moment Map in Geodesic Calculus
33. The Parasymplectic Space of Geodesics Trajectories
34. Diffeomorphisms of Geod(T2)
35. The Diffeomorphisms of the Square
36. Diffeological Spaces are Locally Connected
37. Vague Adjunction of a Point to a Space
38. Embedding a Diffeological Space Into its Powerset
39. Foliations and Diffeology
40. Klein Stratiffcation of Diffeological Spaces
41. Lagrange’s Equations of Motion
42. Poisson Bracket in Diffeology
43. Smooth embeddings and smoothly embedded subsets
44. Seifert Orbifolds
45. Symplectic spaces without Hamiltonian diffeomorphisms
46. The Diffeology Framework of General Covariance
47. Postface: The Beginning of Diffeological Spaces
48. Appendix: A Categorical Approach to Diffeology
49. Bibliography