廣義微分幾何講義-英文 帕特里克.伊格萊西亞斯-澤穆爾 9787523218419 【台灣高等教育出版社】

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書名：廣義微分幾何講義-英文
ISBN：9787523218419
出版社：世界圖書出版
著編譯者：帕特里克.伊格萊西亞斯-澤穆爾
頁數：378
所在地：中國大陸 *此為代購商品
書號：1719474
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內容簡介

《廣義微分幾何講義》是為對微分幾何感興趣的學生準備的，尤其是那些在經典理論未涵蓋的幾何情形。它是已出版的《廣義微分幾何》（Diffeology）的配套教學筆記，一半源自作者在汕頭大學訪問時的專題講座，一半則是作者在同各方學者多年研究探討后的研究成果、思考、練習等作者希望與讀者分享的筆記。全書以時間線為軸，講述Diffeology領域的起源和發展，編排合理，每章篇頭都有總述、定義、理論等講解，輔以推論過程，由簡到難，自然過渡到結論，很符合授課講義的風格，其後還有習題、問題、思考探討等用以鞏固講義知識，並啟發思考，對研究微分幾何或數學物理的學生與研究人員非常有用。

目錄

Preface
Acknowledgements
At the Beginning
1 Differentiable and smooth paths
2 Smooth maps， the holistic approach
3 Diferentiable maps， the pedestrian approach
4 Higher order derivatives and smooth maps
5 The tangent linear map
6 Higher derivatives components
7 The category of Euclidean domains
8 Some theorems we should know
Diffeology，the Axiomatic
9 What is a diffeology?
10 Category {Diffeology}
11 Order in diffeology
12 Pushing and pulling diffeology
13 Making sum of diffeologies
14 Grow and multiply
The Irrational Tori
15 What is a torus?
16 The irrational torus Ta
17 The general codimension 1 case
Generating Families， Dimension
18 Generating famillies toelquyu oJ
19 Dimension of a diffeology
20 Dimension map of a diffeological space
21 Examples of the half-lines
Cartan-De-Rham Calculus
22 Smooth forms in Euclidean spaces
23 Differential forms in diffeology
24 Pushing forwards differential forms
25 De Rham cohomology
26 Cubic homology and De Rham cohomology
Diffeology Fiber Bundles
27 Diffeological fiber bundles， the pedestrian approach g
28 Diffeological fber bundles， the groupoid approach
29 Associated fiber bundles
30 Covering diffeological spaces
31 Examples of diffeological fiber bundles
Homotopy Theory in Diffeology
32 Smooth paths and operationsgmoo avdsvlzeb redNT
33 Every topological space admits a universal covering
34 Relative homotopy
Local Diffeology， Modeling
35 Local diffeology
36 Manifolds
37 Manifolds with boundary
38 Manifolds with corners 30
Modeling:Manifolds， Orbifolds and Quasifolds
39 Orbifolds， the Satake definition
40 Orbifolds as diffeologies
41 Equivalence between V-manifolds and D-orbifolds
42 Internal structure of a D-orbifold
43 Quasifolds as diffeologies
Symplectic Mechanics and Diffeology
44 The short approach to symplectic mechanics
45 Presymplectic and symplectic manifoldsezdue eri no a
46 Symmetries and moment map
47 Coadjoint orbits
48 The classic moment map
49 Geometric quantization
50 Symplectic diffeology
Diffeology and Non-Commutative Geometry
51 Orbifolds and quasifolds again
52 Structure groupoids
53 The C*-algebra
Functional Diffeology on Fourier Coefficients niC esinotlimsH
Smooth Function on Periodic Functions
Symplectic Diffeology on Smooth Periodic Functions
54 A primitive of the symplectic form
55 Hamiltonian action of the infnite torus
56 Orbits of the Hamiltonian flow
57 Reduction of a moment map level
Infinite Torus Action on Smooth Periodic Functions
Basic 1-Forms on Principal Fiber Bundles
Differential of Holonomy for Torus Bundles
58 Loops bundles
59 Holonomy function
Non-symplectic manifold with injective univ moment map
On Riemannian Metric in Diffeology
60 Pointed or pointwise diffeology pe onu lo emeirlqomos)
61 Smooth covariant tensor
62 Riemannian metric on a diffeological space
63 How does this fit?
A Few Half-Lines
1-Forms on Half-Lines
1-Forms on the Subset Half-Line otroalgava bns olpelar
Cotangent Space of the Half-Line
1-Forms on Half-Spaces
p-Forms on Half-Spaces
p-Forms on Corners
64 Smooth structure on corners
65 Application
Differential Forms on the Cross
A note on Hamiltonian Diffeomorphisms
Differential of a Lie-Group Valued Function
66 The general question
67 The Maurer-Cartan form
68 The definition of the differential
The Geodesics of the 2- Torus
The Use of the Moment Map in Geodesic Calculus
69 On geodesics
70 Special metrics on principal bundles
The Parasymplectic Space of Geodesics Trajectories onolol
Diffeomorphisms of Geod(T2)
71 Geodesic trajectories of the 2-torus
72 Diffeomorphisms of Geod(T2)
73 Half a manifold and half not
The Diffeomorphisms of the Square
Diffeological Spaces are Locally Connected
Vague Adjunction of a Point to a Space
Embedding a Diffeological Space Into its Powerset

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