Elements of differential topology:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
CRC Press
2011
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| Series: | A Chapman & Hall book
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| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 301 - 303 |
| Physical Description: | XII, 307 S. graph. Darst. |
| ISBN: | 1439831602 9781439831601 |
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Record in the Search Index
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| adam_text | Titel: Elements of differential topology
Autor: Śāstri, Anant R
Jahr: 2011
Contents
Sectionwise Dependence Tree xii
1 Review of Differential Calculus 1
1.1 Vector Valued Functions ............................ 1
1.2 Directional Derivatives and Total Derivative ................. 3
1.3 Linearity of the Derivative ........................... 13
1.4 Inverse and Implicit Function Theorems.................... 18
1.5 Lagrange Multiplier Method .......................... 26
1.6 Differentiability on Subsets of Euclidean Spaces ............... 33
1.7 Richness of Smooth Maps............................ 38
1.8 Miscellaneous Exercises for Chapter 1..................... 45
2 Integral Calculus 49
2.1 Multivariable Integration ............................ 49
2.2 Sard s Theorem ................................. 54
2.3 Exterior Algebra................................. 57
2.4 Differential Forms ................................ 63
2.5 Exterior Differentiation ............................. 66
2.6 Integration on Singular Chains......................... 69
2.7 Miscellaneous Exercises for Chapter 2..................... 75
3 Submanifolds of Euclidean Spaces 77
3.1 Basic Notions .................................. 77
3.2 Manifolds with Boundary............................ 80
3.3 Tangent Space.................................. 83
3.4 Special Types of Smooth Maps......................... 87
3.5 Transversality .................................. 93
3.6 Homotopy and Stability............................. 95
3.7 Miscellaneous Exercises for Chapter 3..................... 97
4 Integration on Manifolds 101
4.1 Orientation on Manifolds ............................ 101
4.2 Differential Forms on Manifolds ........................ 106
4.3 Integration on Manifolds ............................ 107
4.4 De Rham Cohomology ............................. 113
4.5 Miscellaneous Exercises for Chapter 4..................... 120
5 Abstract Manifolds 121
5.1 Topological Manifolds.............................. 121
5.2 Abstract Differential Manifolds......................... 124
5.3 Gluing Lemma.................................. 129
5.4 Classification of 1-dimensional Manifolds ................... 133
ix
5.5 Tangent Space and Tangent Bündle ...................... 136
5.6 Tangents as Operators ............................. 141
5.7 Whitney Embedding Theorems......................... 145
5.8 Miscellaneous Exercises for Chapter 5..................... 150
6 Isotopy 153
6.1 Normal Bündle and Tubulär Neighborhoods ................. 153
6.2 Orientation on Normal Bündle......................... 158
6.3 Vector Fields and Isotopies........................... 160
6.4 Patching-up Diffeomorphisms.......................... 169
6.5 Miscellaneous Exercises for Chapter 6..................... 174
7 Intersection Theory 177
7.1 Transverse Homotopy Theorem......................... 177
7.2 Oriented Intersection Number ......................... 179
7.3 Degree of a Map................................. 181
7.4 Nonoriented Case ................................ 187
7.5 Winding Number and Separation Theorem .................. 188
7.6 Borsuk-Ulam Theorem ............................. 192
7.7 Hopf Degree Theorem.............................. 194
7.8 Lefschetz Theory................................. 197
7.9 Some Applications................................ 205
7.10 Miscellaneous Exercises for Chapter 7..................... 207
8 Geometry of Manifolds 209
8.1 Morse Functions................................. 209
8.2 Morse Lemma .................................. 213
8.3 Operations on Manifolds ............................ 217
8.4 Further Geometry of Morse Functions..................... 226
8.5 Classification of Compact Surfaces....................... 234
9 Lie Groups and Lie Algebras: The Basics 243
9.1 Review of Some Matrix Theory ........................ 243
9.2 Topological Groups............................... 252
9.3 Lie Groups.................................... 257
9.4 Lie Algebras ................................... 261
9.5 Canonical Coordinates ............................. 265
9.6 Topological Invariance.............................. 270
9.7 Closed Subgroups ................................ 271
9.8 The Adjoint Action ............................... 272
9.9 Existence of Lie Subgroups........................... 274
9.10 Foüation ..................................... 279
Hints/Solutions to Select Exercises 285
Bibliography 301
Index 305
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| any_adam_object | 1 |
| author | Śāstri, Anant R. |
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| dewey-full | 514.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.72 |
| dewey-search | 514.72 |
| dewey-sort | 3514.72 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 1439831602 9781439831601 |
| language | English |
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| physical | XII, 307 S. graph. Darst. |
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| series2 | A Chapman & Hall book |
| spelling | Śāstri, Anant R. Verfasser (DE-588)1013824709 aut Elements of differential topology Anant R. Shastri Boca Raton, Fla. [u.a.] CRC Press 2011 XII, 307 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Chapman & Hall book Literaturverz. S. 301 - 303 Differentialtopologie (DE-588)4012255-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Differentialtopologie (DE-588)4012255-4 s DE-604 DE-601 pdf/application http://zbmath.org/?q=an:1222.57001 Zentralblatt MATH Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026215037&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Śāstri, Anant R. Elements of differential topology Differentialtopologie (DE-588)4012255-4 gnd |
| subject_GND | (DE-588)4012255-4 (DE-588)4123623-3 |
| title | Elements of differential topology |
| title_auth | Elements of differential topology |
| title_exact_search | Elements of differential topology |
| title_full | Elements of differential topology Anant R. Shastri |
| title_fullStr | Elements of differential topology Anant R. Shastri |
| title_full_unstemmed | Elements of differential topology Anant R. Shastri |
| title_short | Elements of differential topology |
| title_sort | elements of differential topology |
| topic | Differentialtopologie (DE-588)4012255-4 gnd |
| topic_facet | Differentialtopologie Lehrbuch |
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