Differentiable manifolds:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2001
|
| Edition: | 2. ed. |
| Series: | Birkhäuser advanced texts
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 418 S. graph. Darst. |
| ISBN: | 9780817641344 9780817647667 3764341343 0817641343 |
Staff View
MARC
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| 100 | 1 | |a Conlon, Lawrence |d 1933- |e Verfasser |0 (DE-588)122970721 |4 aut | |
| 245 | 1 | 0 | |a Differentiable manifolds |c Lawrence Conlon |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2001 | |
| 300 | |a XII, 418 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Birkhäuser advanced texts | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Differenzierbare Mannigfaltigkeit | |
| 650 | 7 | |a Geometria differenziale |2 sbt | |
| 650 | 4 | |a Differentiable manifolds | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-009435245 | ||
Record in the Search Index
| _version_ | 1804128624838705152 |
|---|---|
| adam_text | Contents
Preface
to the Second Edition
xi
Acknowledgments
xiii
Chapter
1.
Topological Manifolds
1
1.1.
Locally Euclidean Spaces
1
1.2.
Topological Manifolds
3
1.3.
Quotient Constructions and 2-Manifolds
6
1.4.
Partitions of Unity
17
1.5.
Imbeddings and Immersions
20
1.6.
Manifolds with Boundary
22
1.7.
Covering Spaces and the Fundamental Group
26
Chapter
2.
The Local Theory of Smooth Functions
41
2.1.
Differentiability Classes
41
2.2.
Tangent Vectors
42
2.3.
Smooth Maps and their Differentials
50
2.4.
Diffeomorphisms and Maps of Constant Rank
54
2.5.
Smooth Submanifolds of Euclidean Space
58
2.6.
Constructions of Smooth Functions
62
2.7.
Smooth Vector Fields
65
2.8.
Local Flows
71
2.9.
Critical Points and Critical Values
80
Chapter
3.
The Global Theory of Smooth Functions
87
3.1.
Smooth Manifolds and Mappings
87
3.2.
Diffeomorphic Structures
93
3.3.
The Tangent Bundle
94
3.4.
Cocycles and Geometric Structures
98
3.5.
Global Constructions of Smooth Functions
104
3.6.
Smooth Manifolds with Boundary
107
3.7.
Smooth Submanifolds
110
3.8.
Smooth Homotopy and Smooth Approximations
116
3.9.
Degree Theory Modulo
2* 119
З.ІО.Могее
Functions*
124
Chapter
4.
Flows and Foliations
131
4.1.
Complete Vector Fields
131
4.2.
The Gradient Flow and Morse Functions*
136
4.3.
The Lie Bracket
142
4.4.
Commuting Flows
145
4.5.
Foliations
150
6.3.
Line Integrals
6.4.
The First Cohomology Space
6.5.
Degree Theory on S1*
Chapter
7.
Multilinear Algebra and Tensors
7.1.
Tensor Algebra
7.2.
Exterior Algebra
7.3.
Symmetric Algebra
7.4.
Multilinear Bundle Theory
7.5.
The Module of Sections
viii
CONTENTS
Chapter
5.
Lie Groups and Lie Algebras
161
5.1.
Basic Definitions and Facts
161
5.2.
Lie Subgroups and Subalgebras
170
5.3.
Closed Subgroups*
173
5.4.
Homogeneous Spaces*
178
Chapter
6.
Co vectors and 1-Forms
183
6.1.
Dual Bundles
183
6.2.
The space of l-forms
185
190
195
202
209
209
217
226
227
230
Chapter
8.
Integration of Forms and
de Rham
Cohomology
239
8.1.
The Exterior Derivative
239
8.2.
Stokes Theorem and Singular Homology
245
8.3.
The
Poincaré
Lemma
258
8.4.
Exact Sequences
264
8.5.
Mayer-Vietoris Sequences
267
8.6.
Computations of Cohomology
271
8.7.
Degree Theory*
274
8.8.
Poincaré
Duality*
276
8.9.
The
de Rham
Theorem*
281
Chapter
9.
Forms and Foliations
289
9.1.
The Frobenius Theorem Revisited
289
9.2.
The Normal Bundle and Transversality
293
9.3.
Closed, Nonsingular l-forms*
296
Chapter
10.
Riemannian Geometry
303
10.1.
Connections
304
10.2.
Riemannian Manifolds
311
10.3.
Gauss Curvature
315
10.4.
Complete Riemannian Manifolds
322
10.5.
Geodesic Convexity
334
10.6.
The Cartan Structure Equations
337
10.7.
Riemannian Homogeneous Spaces*
342
Chapter
11.
Principal Bundles*
347
11.1.
The Frame Bundle
347
11.2.
Principal G-Bundles
351
11.3.
Cocycles and Reductions
354
11.4.
Frame Bundles and the Equations of Structure
357
CONTENTS ix
Appendix A. Construction of the Universal Covering
369
Appendix B. The Inverse Function Theorem
373
Appendix C. Ordinary Differential Equations
379
C.I. Existence and uniqueness of solutions
379
C.2. A digression concerning Banach spaces
382
C.3. Smooth dependence on initial conditions
383
C.4. The Linear Case
385
Appendix D. The
de Rham
Cohomology Theorem
387
D.I.
Cech
cohomology
387
D.2. The
de Rham-Cech
complex
391
D.3. Singular Cohomology
397
Bibliography
403
Index
405
|
| any_adam_object | 1 |
| author | Conlon, Lawrence 1933- |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 350 SK 370 |
| ctrlnum | (OCoLC)248225977 (DE-599)BVBBV013799740 |
| dewey-full | 516.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.6 |
| dewey-search | 516.6 |
| dewey-sort | 3516.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T18:52:12Z |
| institution | BVB |
| isbn | 9780817641344 9780817647667 3764341343 0817641343 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009435245 |
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| physical | XII, 418 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Birkhäuser advanced texts |
| spelling | Conlon, Lawrence 1933- Verfasser (DE-588)122970721 aut Differentiable manifolds Lawrence Conlon 2. ed. Boston [u.a.] Birkhäuser 2001 XII, 418 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Birkhäuser advanced texts Hier auch später erschienene, unveränderte Nachdrucke Differenzierbare Mannigfaltigkeit Geometria differenziale sbt Differentiable manifolds Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd rswk-swf Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009435245&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Conlon, Lawrence 1933- Differentiable manifolds Differenzierbare Mannigfaltigkeit Geometria differenziale sbt Differentiable manifolds Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd |
| subject_GND | (DE-588)4012269-4 |
| title | Differentiable manifolds |
| title_auth | Differentiable manifolds |
| title_exact_search | Differentiable manifolds |
| title_full | Differentiable manifolds Lawrence Conlon |
| title_fullStr | Differentiable manifolds Lawrence Conlon |
| title_full_unstemmed | Differentiable manifolds Lawrence Conlon |
| title_short | Differentiable manifolds |
| title_sort | differentiable manifolds |
| topic | Differenzierbare Mannigfaltigkeit Geometria differenziale sbt Differentiable manifolds Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd |
| topic_facet | Differenzierbare Mannigfaltigkeit Geometria differenziale Differentiable manifolds |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009435245&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT conlonlawrence differentiablemanifolds |