Mapping degree theory:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI [u.a.]
American Mathematical Society [u.a.]
2009
|
| Series: | Graduate studies in mathematics
108 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | X, 244 S. graph. Darst. |
| ISBN: | 9780821849156 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804145499516698624 |
|---|---|
| adam_text | Titel: Mapping degree theory
Autor: Outerelo, Enrique
Jahr: 2009
Contents
Preface
IX
I. History 1
1. Prehistory............................. 1
2. Inception and formation ..................... 14
3. Accomplishment.......................... 28
4. Renaissance and reformation................... 35
5. Axiomatization .......................... 38
6. Further developments....................... 42
II. Manifolds 49
1. Differentiable mappings...................... 49
2. Differentiable manifolds...................... 53
3. Regular values........................... 62
4. Tubular neighborhoods...................... 67
5. Approximation and homotopy.................. 75
6. Diffeotopies............................. 80
7. Orientation............................. 84
III. The Brouwer-Kronecker degree 95
1. The degree of a smooth mapping................. 95
2. The de Rham definition ...................... 103
3. The degree of a continuous mapping............... 110
vii
4. The degree of a differentiable mapping ............. 114
5. The Hopf invariant ........................ 119
6. The Jordan Separation Theorem................. 124
7. The Brouwer Theorems...................... 133
IV. Degree theory in Euclidean spaces 137
1. The degree of a smooth mapping................. 137
2. The degree of a continuous mapping............... 145
3. The degree of a differentiable mapping............. 153
4. Winding number.......................... 156
5. The Borsuk-Ulam Theorem.................... 160
6. The Multiplication Formula ................... 171
7. The Jordan Separation Theorem................. 176
V. The Hopf Theorems 183
1. Mappings into spheres....................... 183
2. The Hopf Theorem: Brouwer-Kronecker degree......... 191
3. The Hopf Theorem: Euclidean degree.............. 196
4. The Hopf fibration......................... 200
5. Singularities of tangent vector fields............... 206
6. Gradient vector fields....................... 211
7. The Poincare-Hopf Index Theorem................ 218
Names of mathematicians cited 225
Historical references 227
Bibliography 233
Symbols 235
Index 239
|
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| author | Outerelo, Enrique 1939- Ruiz, Jesús M. 1957- |
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| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV026864410 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:20:25Z |
| institution | BVB |
| isbn | 9780821849156 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022391828 |
| oclc_num | 698813712 |
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| owner_facet | DE-188 DE-19 DE-BY-UBM |
| physical | X, 244 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | American Mathematical Society [u.a.] |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Outerelo, Enrique 1939- Verfasser (DE-588)140229361 aut Mapping degree theory Enrique Outerelo ; Jesús M. Ruiz Providence, RI [u.a.] American Mathematical Society [u.a.] 2009 X, 244 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 108 Includes bibliographical references and index Abbildungsgrad (DE-588)4140975-9 gnd rswk-swf Abbildungsgrad (DE-588)4140975-9 s DE-604 Ruiz, Jesús M. 1957- Verfasser (DE-588)113233264 aut Graduate studies in mathematics 108 (DE-604)BV009739289 108 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022391828&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Outerelo, Enrique 1939- Ruiz, Jesús M. 1957- Mapping degree theory Graduate studies in mathematics Abbildungsgrad (DE-588)4140975-9 gnd |
| subject_GND | (DE-588)4140975-9 |
| title | Mapping degree theory |
| title_auth | Mapping degree theory |
| title_exact_search | Mapping degree theory |
| title_full | Mapping degree theory Enrique Outerelo ; Jesús M. Ruiz |
| title_fullStr | Mapping degree theory Enrique Outerelo ; Jesús M. Ruiz |
| title_full_unstemmed | Mapping degree theory Enrique Outerelo ; Jesús M. Ruiz |
| title_short | Mapping degree theory |
| title_sort | mapping degree theory |
| topic | Abbildungsgrad (DE-588)4140975-9 gnd |
| topic_facet | Abbildungsgrad |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022391828&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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