Fundamental groups and covering spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Portuguese |
| Published: |
Natick, Mass.
Peters
2003
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Portug. übers. |
| Physical Description: | IX, 210 S. graph. Darst. |
| ISBN: | 1568811314 |
Staff View
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| 650 | 4 | |a Recouvrements (Espaces topologiques) | |
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| 650 | 4 | |a Algebraic topology | |
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Record in the Search Index
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|---|---|
| adam_text | FUNDAMENTAL GROUPS AND COVERING SPACES ELON LAGES LIMA TRANSLATED BY
JONAS GOMES A K PETERS NATICK, MASSACHUSETTS CONTENTS PREFACE IX I
FUNDAMENTAL GROUPS 1 1 HOMOTOPY 3 1.1 HOMOTOPIC MAPS 3 1.1.1 VECTOR
FIELDS ON SPHERES 6 1.2 HOMOTOPY TYPE 10 1.3 CONTRACTIBLE SPACES 11 1.4
HOMOTOPY AND MAP EXTENSION 13 1.4.1 EUCLIDEAN NEIGHBORHOOD RETRACTS 14
1.5 TREES -.... 17 1.6 HOMOTOPY OF PAIRS AND RELATIVE HOMOTOPY 20 1.7
EXERCISES 20 2 THE FUNDAMENTAL GROUP 25 2.1 PATH HOMOTOPY 25 2.1.1
OPERATIONS WITH PATHS 28 2.1.2 HOMOTOPY AND PATH DECOMPOSITION 32 2.2
THE FUNDAMENTAL GROUP 33 2.3 THE INDUCED HOMOMORPHISM 34 2.4 OTHER
DESCRIPTIONS OF THE FUNDAMENTAL GROUP 39 2.4.1 SPACES WITH ABELIAN
FUNDAMENTAL GROUP 39 2.4.2 THE FUNDAMENTAL GROUP AND MAPS FROM S 1 TO X
. . 39 VI CONTENTS 2.5 SIMPLY CONNECTED SPACES 40 2.6 SOME PROPERTIES OF
THE FUNDAMENTAL GROUP 44 2.7 TOPOLOGICAL GROUPS 47 2.8 EXERCISES 49 3
SOME EXAMPLES AND APPLICATIONS 53 3.1 THE FUNDAMENTAL GROUP OF THE
CIRCLE 53 3.2 THE ISOMORPHISM TT^S 1 ) Z 60 3.3 REAL PROJECTIVE SPACES
62 3.4 FIBRATIONS AND COMPLEX PROJECTIVE SPACES 67 3.5 EXERCISES 71 4
CLASSICAL MATRIX GROUPS 73 4.1 ROTATIONS IN EUCLIDEAN SPACE 73 4.2 THE
GROUPS SU(N) AND SP(N) 80 4.3 EXERCISES 91 5 THE WINDING NUMBER 95 5.1
THE WINDING NUMBER OF A CLOSED PLANE CURVE 95 5.2 THE GRAUSTEIN-WHITNEY
THEOREM 98 5.2.1 ABOUT EVERSIONS 103 5.3 THE WINDING NUMBER AS A
CURVILINEAR INTEGRAL 105 5.3.1 THE WINDING NUMBER AS A COMPLEX INTEGRAL
. . . . 109 5.4 WINDING NUMBER AND POLYNOMIAL ROOTS 110 5.5 EXERCISES
114 COVERING SPACES 117 COVERING SPACES 119 6.1 LOCAL HOMEOMORPHISMS AND
LIFTINGS 119 6.2 COVERING MAPS 124 6.3 PROPERLY DISCONTINUOUS GROUPS 129
6.4 PATH LIFTING AND HOMOTOPIES 134 6.4.1 AN APPLICATION 143 6.5
DIFFERENTIABLE COVERINGS 144 6.6 EXERCISES 147 COVERING MAPS AND
FUNDAMENTAL GROUPS 151 7.1 THE CONJUGATE CLASS OF A COVERING MAP 151 7.2
THE FUNDAMENTAL LIFTING THEOREM 156 7.3 HOMOMORPHISMS OF COVERING SPACES
161 7.4 COVERING AUTOMORPHISMS 166 CONTENTS VII 7.5 PROPERLY
DISCONTINUOUS GROUPS AND REGULAR COVERINGS . . . 171 7.6 EXISTENCE OF
COVERINGS 172 7.7 FUNDAMENTAL GROUP OF A COMPACT SURFACE 173 7.8
EXERCISES 179 8 ORIENTED DOUBLE COVERING 183 8.1 ORIENTATION OF A VECTOR
SPACE 183 8.2 ORIENTABLE MANIFOLDS 185 8.3 PROPERLY DISCONTINUOUS GROUPS
OF DIFFEOMORPHISMS 190 8.4 ORIENTED DOUBLE COVERING 192 8.5 RELATIONS
WITH THE FUNDAMENTAL GROUP 197 8.6 EXERCISES 198 APPENDIX: PROPER MAPS
201 BIBLIOGRAPHY 205 INDEX 207
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| dewey-ones | 514 - Topology |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T20:00:10Z |
| institution | BVB |
| isbn | 1568811314 |
| language | English Portuguese |
| lccn | 2003048719 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012892019 |
| oclc_num | 52001487 |
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| owner | DE-824 DE-83 DE-11 |
| owner_facet | DE-824 DE-83 DE-11 |
| physical | IX, 210 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Peters |
| record_format | marc |
| spelling | Lima, Elon Lages 1929-2017 Verfasser (DE-588)172485592 aut Grupo fundamental e espaços de recobrimento Fundamental groups and covering spaces Elon Lages Lima Natick, Mass. Peters 2003 IX, 210 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Aus dem Portug. übers. Groupe fondamental (Mathématiques) Recouvrements (Espaces topologiques) Topologie algébrique Algebraic topology Covering spaces (Topology) Fundamental groups (Mathematics) Fundamentalgruppe (DE-588)4155638-0 gnd rswk-swf Fundamentalgruppe (DE-588)4155638-0 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012892019&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lima, Elon Lages 1929-2017 Fundamental groups and covering spaces Groupe fondamental (Mathématiques) Recouvrements (Espaces topologiques) Topologie algébrique Algebraic topology Covering spaces (Topology) Fundamental groups (Mathematics) Fundamentalgruppe (DE-588)4155638-0 gnd |
| subject_GND | (DE-588)4155638-0 |
| title | Fundamental groups and covering spaces |
| title_alt | Grupo fundamental e espaços de recobrimento |
| title_auth | Fundamental groups and covering spaces |
| title_exact_search | Fundamental groups and covering spaces |
| title_full | Fundamental groups and covering spaces Elon Lages Lima |
| title_fullStr | Fundamental groups and covering spaces Elon Lages Lima |
| title_full_unstemmed | Fundamental groups and covering spaces Elon Lages Lima |
| title_short | Fundamental groups and covering spaces |
| title_sort | fundamental groups and covering spaces |
| topic | Groupe fondamental (Mathématiques) Recouvrements (Espaces topologiques) Topologie algébrique Algebraic topology Covering spaces (Topology) Fundamental groups (Mathematics) Fundamentalgruppe (DE-588)4155638-0 gnd |
| topic_facet | Groupe fondamental (Mathématiques) Recouvrements (Espaces topologiques) Topologie algébrique Algebraic topology Covering spaces (Topology) Fundamental groups (Mathematics) Fundamentalgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012892019&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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