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Geometry of differential forms /
~
Morita, Shigeyuki, (1946-)
Geometry of differential forms /
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Geometry of differential forms /Shigeyuki Morita ; translated by Teruko Nagase, Katsumi Nomizu.
作者:
Morita, Shigeyuki,
出版者:
Providence, R.I. :American Mathematical Society,©2001.
面頁冊數:
xxiv, 321 pages :illustrations ;22 cm
標題:
Differential forms.
電子資源:
Kostenfrei
ISBN:
0821810456
Geometry of differential forms /
Morita, Shigeyuki,1946-
Geometry of differential forms /
Shigeyuki Morita ; translated by Teruko Nagase, Katsumi Nomizu. - Providence, R.I. :American Mathematical Society,©2001. - xxiv, 321 pages :illustrations ;22 cm - Translations of mathematical monographs,v. 2010065-9282 ;. - Translations of mathematical monographs ;v. 201..
Includes bibliographical references (pages 315-316) and index.
Outline and Goal of the Theoryxix --
ISBN: 0821810456
Standard No.: 9780821810453
LCCN: 2001022608
Nat. Bib. Agency Control No.: 006567577UkSubjects--Topical Terms:
190957
Differential forms.
LC Class. No.: QA381 / .M6713 2001
Dewey Class. No.: 515/.37
Geometry of differential forms /
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Bibun keishiki no kikagaku.
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English
245
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Geometry of differential forms /
$c
Shigeyuki Morita ; translated by Teruko Nagase, Katsumi Nomizu.
260
$a
Providence, R.I. :
$b
American Mathematical Society,
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©2001.
300
$a
xxiv, 321 pages :
$b
illustrations ;
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22 cm
336
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text
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0065-9282 ;
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490
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Iwanami series in modern mathematics
504
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Includes bibliographical references (pages 315-316) and index.
505
0 0
$t
Outline and Goal of the Theory
$g
xix --
$g
Chapter 1
$t
Manifolds
$g
1 --
$g
(a)
$t
N-dimensional numerical space R[superscript n]
$g
2 --
$g
(b)
$t
Topology of R[superscript n]
$g
3 --
$g
(c)
$t
C[infinity] functions and diffeomorphisms
$g
4 --
$g
(d)
$t
Tangent vectors and tangent spaces of R[superscript n]
$g
6 --
$g
(e)
$t
Necessity of an abstract definition
$g
10 --
$g
1.2
$t
Definition and examples of manifolds
$g
11 --
$g
(a)
$t
Local coordinates and topological manifolds
$g
11 --
$g
(b)
$t
Definition of differentiable manifolds
$g
13 --
$g
(c)
$t
R[superscript n] and general surfaces in it
$g
16 --
$g
(d)
$t
Submanifolds
$g
19 --
$g
(e)
$t
Projective spaces
$g
21 --
$g
(f)
$t
Lie groups
$g
22 --
$g
1.3
$t
Tangent vectors and tangent spaces
$g
23 --
$g
(a)
$t
C[infinity] functions and C[infinity] mappings on manifolds
$g
23 --
$g
(b)
$t
Practical construction of C[infinity] functions on a manifold
$g
25 --
$g
(c)
$t
Partition of unity
$g
27 --
$g
(d)
$t
Tangent vectors
$g
29 --
$g
(e)
$t
Differential of maps
$g
33 --
$g
(f)
$t
Immersions and embeddings
$g
34 --
$g
1.4
$t
Vector fields
$g
36 --
$g
(a)
$t
Vector fields
$g
36 --
$g
(b)
$t
Bracket of vector fields
$g
38 --
$g
(c)
$t
Integral curves of vector fields and one-parameter group of local transformations
$g
39 --
$g
(d)
$t
Transformations of vector fields by diffeomorphism
$g
44 --
$g
1.5
$t
Fundamental facts concerning manifolds
$g
44 --
$g
(a)
$t
Manifolds with boundary
$g
44 --
$g
(b)
$t
Orientation of a manifold
$g
46 --
$g
(c)
$t
Group actions
$g
49 --
$g
(d)
$t
Fundamental groups and covering manifolds
$g
51 --
$g
Chapter 2
$t
Differential Forms
$g
57 --
$g
2.1
$t
Definition of differential forms
$g
57 --
$g
(a)
$t
Differential forms on R[superscript n]
$g
57 --
$g
(b)
$t
Differential forms on a general manifold
$g
61 --
$g
(c)
$t
Exterior algebra
$g
61 --
$g
(d)
$t
Various definitions of differential forms
$g
66 --
$g
2.2
$t
Various operations on differential forms
$g
69 --
$g
(a)
$t
Exterior product
$g
69 --
$g
(b)
$t
Exterior differentiation
$g
70 --
$g
(c)
$t
Pullback by a map
$g
72 --
$g
(d)
$t
Interior product and Lie derivative
$g
72 --
$g
(e)
$t
Cartan formula and properties of Lie derivatives
$g
73 --
$g
(f)
$t
Lie derivative and one-parameter group of local transformations
$g
77 --
$g
2.3
$t
Frobenius theorem
$g
80 --
$g
(a)
$t
Frobenius theorem--Representation by vector fields
$g
80 --
$g
(b)
$t
Commutative vector fields
$g
82 --
$g
(c)
$t
Proof of the Frobenius theorem
$g
83 --
$g
(d)
$t
Frobenius theorem--Representation by differential forms
$g
86 --
$g
(a)
$t
Differential forms with values in a vector space
$g
89 --
$g
(b)
$t
Maurer-Cartan form of a Lie group
$g
90 --
$g
Chapter 3
$t
De Rham Theorem
$g
95 --
$g
3.1
$t
Homology of manifolds
$g
96 --
$g
(a)
$t
Homology of simplicial complexes
$g
96 --
$g
(b)
$t
Singular homology
$g
99 --
$g
(c)
$t
C[infinity] triangulation of C[infinity] manifolds
$g
100 --
$g
(d)
$t
C[infinity] singular chain complexes of C[infinity] manifolds
$g
103 --
$g
3.2
$t
Integral of differential forms and the Stokes theorem
$g
104 --
$g
(a)
$t
Integral of n-forms on n-dimensional manifolds
$g
104 --
$g
(b)
$t
Stokes theorem (in the case of manifolds)
$g
107 --
$g
(c)
$t
Integral of differential forms on chains, and the Stokes theorem
$g
109 --
$g
3.3
$t
De Rham theorem
$g
111 --
$g
(a)
$t
de Rham cohomology
$g
111 --
$g
(b)
$t
De Rham theorem
$g
113 --
$g
(c)
$t
Poincare lemma
$g
116 --
$g
3.4
$t
Proof of the de Rham theorem
$g
119 --
$g
(a)
$t
Cech cohomology
$g
119 --
$g
(b)
$t
Comparison of de Rham cohomology and Cech cohomology
$g
121 --
$g
(c)
$t
Proof of the de Rham theorem
$g
126 --
$g
(d)
$t
De Rham theorem and product structure
$g
131 --
$g
3.5
$t
Applications of the de Rham theorem
$g
133 --
$g
(a)
$t
Hopf invariant
$g
133 --
$g
(b)
$t
Massey product
$g
136 --
$g
(c)
$t
Cohomology of compact Lie groups
$g
137 --
$g
(d)
$t
Mapping degree
$g
138 --
$g
(e)
$t
Integral expression of the linking number by Gauss
$g
140 --
$g
Chapter 4
$t
Laplacian and Harmonic Forms
$g
145 --
$g
4.1
$t
Differential forms on Riemannian manifolds
$g
145 --
$g
(a)
$t
Riemannian metric
$g
145 --
$g
(b)
$t
Riemannian metric and differentieal forms
$g
148 --
$g
(c)
$t
*-operator of Hodge
$g
150 --
$g
4.2
$t
Laplacian and harmonic forms
$g
153 --
$g
4.3
$t
Hodge theorem
$g
158 --
$g
(a)
$t
Hodge theorem and the Hodge decomposition of differential forms
$g
158 --
$g
(b)
$t
Idea for the proof of the Hodoge decomposition
$g
160 --
$g
4.4
$t
Applications of the Hodge theorem
$g
162 --
$g
(a)
$t
Poincare duality theorem
$g
162 --
$g
(b)
$t
Manifolds and Euler number
$g
164 --
$g
(c)
$t
Intersection number
$g
165 --
$g
Chapter 5
$t
Vector Bundles and Characteristic Classes
$g
169 --
$g
5.1
$t
Vector bundles
$g
169 --
$g
(a)
$t
Tangent bundle of a manifold
$g
169 --
$g
(b)
$t
Vector bundles
$g
170 --
$g
(c)
$t
Several constructions of vector bundles
$g
173 --
$g
5.2
$t
Geodesics and parallel translation of vectors
$g
180 --
$g
(a)
$t
Geodesics
$g
180 --
$g
(b)
$t
Covariant derivative
$g
181 --
$g
(c)
$t
Parallel displacement of vectors and curvature
$g
183 --
$g
5.3
$t
Connections in vector bundles and
$g
185 --
$g
(a)
$t
Connections
$g
185 --
$g
(b)
$t
Curvature
$g
186 --
$g
(c)
$t
Connection form and curvature form
$g
188 --
$g
(d)
$t
Transformation rules of the local expressions for a connection and its curvature
$g
190 --
$g
(e)
$t
Differential forms with values in a vector bundle
$g
191 --
$g
5.4
$t
Pontrjagin classes
$g
193 --
$g
(a)
$t
Invariant polynomials
$g
193 --
$g
(b)
$t
Definition of Pontrjagin classes
$g
197 --
$g
(c)
$t
Levi-Civita connection
$g
201 --
$g
5.5
$t
Chern classes
$g
204 --
$g
(a)
$t
Connection and curvature in a complex vector bundle
$g
204 --
$g
(b)
$t
Definition of Chern classes
$g
205 --
$g
(c)
$t
Whitney formula
$g
207 --
$g
(d)
$t
Relations between Pontrjagin and Chern classes
$g
208 --
$g
5.6
$t
Euler classes
$g
211 --
$g
(a)
$t
Orientation of vector bundles
$g
211 --
$g
(b)
$t
Definition of the Euler class
$g
211 --
$g
(c)
$t
Properties of the Euler class
$g
214 --
$g
5.7
$t
Applications of characteristic classes
$g
216 --
$g
(a)
$t
Gauss-Bonnet theorem
$g
216 --
$g
(b)
$t
Characteristic classes of the complex projective space
$g
223 --
$g
(c)
$t
Characteristic numbers
$g
225 --
$g
Chapter 6
$t
Fiber Bundles and Characteristic Classes
$g
231 --
$g
6.1
$t
Fiber bundle and principal bundle
$g
231 --
$g
(a)
$t
Fiber bundle
$g
231 --
$g
(b)
$t
Structure group
$g
233 --
$g
(c)
$t
Principal bundle
$g
236 --
$g
(d)
$t
Classification of fiber bundles and characteristic classes
$g
238 --
$g
(e)
$t
Examples of fiber bundles
$g
239 --
$g
6.2
$t
S[superscript 1] bundles and Euler classes
$g
240 --
$g
(a)
$t
S[superscript 1] bundle
$g
241 --
$g
(b)
$t
Euler class of an S[superscript 1] bundle
$g
241 --
$g
(c)
$t
Classification of S[superscript 1] bundles
$g
246 --
$g
(d)
$t
Defining the Euler class for an S[superscript 1] bundle by using differential forms
$g
249 --
$g
(e)
$t
Primary obstruction class and the Euler class of the sphere bundle
$g
254 --
$g
(f)
$t
Vector fields on a manifold and Hopf index theorem
$g
255 --
$g
6.3
$t
Connections
$g
257 --
$g
(a)
$t
Connections in general fiber bundles
$g
257 --
$g
(b)
$t
Connections in principal bundles
$g
260 --
$g
(c)
$t
Differential form representation of a connection in a principal bundle
$g
262 --
$g
6.4
$t
Curvature
$g
265 --
$g
(a)
$t
Curvature form
$g
265 --
$g
(b)
$t
Weil algebra
$g
268 --
$g
(c)
$t
Exterior differentiation of the Weil algebra
$g
270 --
$g
6.5
$t
Characteristic classes
$g
275 --
$g
(a)
$t
Weil homomorphism
$g
275 --
$g
(b)
$t
Invariant polynomials for Lie groups
$g
279 --
$g
(c)
$t
Connections for vector bundles and principal bundles
$g
282 --
$g
(d)
$t
Characterisric classes
$g
284 --
$g
6.6
$t
A couple of items
$g
285 --
$g
(a)
$t
Triviality of the cohomology of the Weil algebra
$g
285 --
$g
(b)
$t
Chern-Simons forms
$g
287 --
$g
(c)
$t
Flat bundles and holonomy homomorphisms
$g
287.
650
0
$a
Differential forms.
$3
190957
650
0
$a
Differentiable manifolds.
$3
190948
650
6
$a
Formes différentiables.
$3
883451
650
6
$a
Variétés différentiables.
$2
ram
$3
883452
830
0
$a
Translations of mathematical monographs ;
$v
v. 201.
$x
0065-9282
$3
883413
830
0
$a
Iwanami series in modern mathematics.
$3
883414
856
4 1
$3
Table of contents
$u
http://www.gbv.de/dms/goettingen/328478911.pdf
$z
Kostenfrei
938
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Baker & Taylor
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BKTY
$c
56.00
$d
60.95
$i
0821810456
$n
0003715358
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active
938
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BROD
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57962715
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$53.00
938
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Baker and Taylor
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BTCP
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2001022608
938
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YBP Library Services
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YANK
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1771958
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