Foundations of differentiable manifolds and Lie groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2000
|
| Ausgabe: | Repr. [d. Ausg.] Glenview, Ill. 1971, 7. print. |
| Schriftenreihe: | Graduate texts in mathematics
94 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 272 S. |
| ISBN: | 3540908943 0387908943 9780387908946 |
Internformat
MARC
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| 264 | 1 | |a New York [u.a.] |b Springer |c 2000 | |
| 300 | |a IX, 272 S. | ||
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| 490 | 1 | |a Graduate texts in mathematics |v 94 | |
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Datensatz im Suchindex
| _version_ | 1804130250423009280 |
|---|---|
| adam_text | ii
MANIFOLDS
2
Preliminaries
5
Differentiable Manifolds
8
The Second Axiom of Countability
11
Tangent Vectors and Differentials
22
Submanifolds, Diffeomorphisms, and the Inverse Function Theorem
30
Implicit Function Theorems
34
Vector Fields
41
Distributions and the Frobenius Theorem
50
Exercises
¿b TENSORS AND DIFFERENTIAL FORMS
54
Tensor and Exterior Algebras
62
Tensor Fields and Differential Forms
69
The Lie Derivative
73
Differential Ideals
77
Exercises
<S> LIE GROUPS
82
Lie Groups and Their Lie Algebras
89
Homomorphisms
92
Lie Subgroups
98
Coverings
101
Simply Connected Lie Groups
102
Exponential Map
109
Continuous Homomorphisms
110
Closed Subgroups
112
The Adjoint Representation
117
Automorphisms and Derivations of Bilinear Operations and Forms
120
Homogeneous Manifolds
132
Exercises
Contents ix
^)
INTEGRATION
ON MANIFOLDS
138
Orientation
140
Integration on Manifolds
153 de Rham
Cohomology
157
Exercises
SHEAVES, COHOMOLOGY, AND THE
DE RHAM
THEOREM
163
Sheaves and Presheaves
173
Cochain Complexes
176
Axiomatic Sheaf Cohomology
The Classical Cohomology Theories
186
Alexander-Spanier
Cohomology
189
de
Rham Cohomology
191
Singular Cohomology
200
Čech
Cohomology
205
The
de Rham
Theorem
207
Multiplicative Structure
214
Supports
216
Exercises
W
THE HODGE THEOREM
220
The Laplace-Beltrami Operator
222
The Hodge Theorem
227
Some Calculus
240
Elliptic Operators
243
Reduction to the Periodic Case
250
Ellipticitv of the Laplace-Beltrami Operator
251
Exercises
260
BIBLIOGRAPHY
262
SUPPLEMENT TO THE BIBLIOGRAPHY
264
INDEX OF NOTATION
267
INDEX
|
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| author | Warner, Frank W. 1938- |
| author_GND | (DE-588)172442966 |
| author_facet | Warner, Frank W. 1938- |
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| bvnumber | BV017437681 |
| classification_rvk | SK 350 |
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| discipline | Mathematik |
| edition | Repr. [d. Ausg.] Glenview, Ill. 1971, 7. print. |
| format | Book |
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| id | DE-604.BV017437681 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:18:03Z |
| institution | BVB |
| isbn | 3540908943 0387908943 9780387908946 |
| language | English |
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| physical | IX, 272 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Warner, Frank W. 1938- Verfasser (DE-588)172442966 aut Foundations of differentiable manifolds and Lie groups Frank W. Warner Repr. [d. Ausg.] Glenview, Ill. 1971, 7. print. New York [u.a.] Springer 2000 IX, 272 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 94 Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content Lie-Gruppe (DE-588)4035695-4 s Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 s 3\p DE-604 DE-604 Graduate texts in mathematics 94 (DE-604)BV000000067 94 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010507940&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Warner, Frank W. 1938- Foundations of differentiable manifolds and Lie groups Graduate texts in mathematics Lie-Gruppe (DE-588)4035695-4 gnd Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4012269-4 (DE-588)4151278-9 (DE-588)4123623-3 |
| title | Foundations of differentiable manifolds and Lie groups |
| title_auth | Foundations of differentiable manifolds and Lie groups |
| title_exact_search | Foundations of differentiable manifolds and Lie groups |
| title_full | Foundations of differentiable manifolds and Lie groups Frank W. Warner |
| title_fullStr | Foundations of differentiable manifolds and Lie groups Frank W. Warner |
| title_full_unstemmed | Foundations of differentiable manifolds and Lie groups Frank W. Warner |
| title_short | Foundations of differentiable manifolds and Lie groups |
| title_sort | foundations of differentiable manifolds and lie groups |
| topic | Lie-Gruppe (DE-588)4035695-4 gnd Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd |
| topic_facet | Lie-Gruppe Differenzierbare Mannigfaltigkeit Einführung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010507940&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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