Algebraic topology:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1989
|
| Ausgabe: | 2. print. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 528 S. |
| ISBN: | 3540906460 0387906460 0387944265 |
Internformat
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| 245 | 1 | 0 | |a Algebraic topology |c Edwin H. Spanier |
| 250 | |a 2. print. | ||
| 264 | 1 | |a New York u.a. |b Springer |c 1989 | |
| 300 | |a XIV, 528 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Datensatz im Suchindex
| _version_ | 1804124423058358272 |
|---|---|
| adam_text | EDWIN H. SPANIER
ALGEBRAIC TOPOLOGY
SPRINGER
CONTENTS
INTRODUCTION I
1
SET THEORY 1
2
GENERAL TOPOLOGY 4
!
3
GROUP THEORY 6
4
MODULES 7
5
EUCLIDEAN SPACES
9
1 HOMOTOPY AND THE FUNDAMENTAL GROUP 12
1
CATEGORIES 14
2
FUNCTORS 18
3
HOMOTOPY 22
4
RETRACTION AND DEFORMATION 27
5
H SPACES 33
6
SUSPENSION 39
7 THE FUNDAMENTAL GROUPOID 45
8
THE FUNDAMENTAL GROUP SO
EXERCISES 56
*** CONTENTS
2 COVERING SPACES AND FIBRATIONS 6O
1
COVERING PROJECTIONS 62
2
THE HOMOTOPY LIFTING PROPERTY 65
3
RELATIONS WITH THE FUNDAMENTAL GROUP 70
4
THE LIFTING PROBLEM 74
5
THE CLASSIFICATION OF COVERING PROJECTIONS 79
6
COVERING TRANSFORMATIONS 85.
7
FIBER BUNDLES 89
8
FIBRATIONS 96
EXERCISES 103
POLYHEDRA 1O6
1
SIMPLIDAL COMPLEXES 108
2
LINEARITY IN SIMPLIDAL COMPLEXES 114
3
SUBDIVISION 121
4
SIMPLIDAL APPROXIMATION 126
5 CONTIGUITY CLASSES 129
6
THE EDGE-PATH GROUPOID 134
I
7
GRAPHS 139
8
EXAMPLES AND APPLICATIONS 143
EXERCISES 149
HOMOLOGY 15
4
1
CHAIN COMPLEXES 156
2
CHAIN HOMOTOPY 162 &
3
THE HOMOLOGY OF SIMPLIDAL COMPLEXES 167
4
SINGULAR HOMOLOGY 173
5
EXACTNESS 179
MAYER-VIETORIS SEQUENCES 186
7
SOME APPLICATIONS OF HOMOLOGY 193
8
AXIOMATIC CHARACTERIZATION OF HOMOLOGY 199
EXERCISES 205
CONTENTS
XITI
5 PRODUCTS 21
1
HOMOLOGY WITH COEFFICIENTS 212
2
THE UNIVERSAL-COEFFIDEHT THEOREM FOR HOMOLOGY 219
3
THE KUNNETH FORMULA 227
4
COHOMOLOGY 236
5 THE UNIVERSAL-COEFFIDENT THEOREM FOR COHOMOLOGY 241
CUP AND CAP PRODUCTS 248
7
HOMOLOGY OF FIBER BUNDLES 255
8
THE COHOMOLOGY ALGEBRA 263
9 THE STEENROD SQUARING OPERATIONS 269
EXERCISES 276
6
GENERAL COHOMOLOG
Y THEORY AN
D DUALITY 284
1
THE SLANT PRODUCT 286
2
DUALITY IN TOPOLOGICAL MANIFOLDS 292 YY
3
THE FUNDAMENTAL CLASS OF A MANIFOLD 299
4
THE ALEXANDER COHOMOLOGY THEORY 306
5
THE HOMOTOPY AXIOM FOR THE ALEXANDER THEORY 311
6
TAUTNESS AND CONTINUITY 315
7
PRESHEAVES 323
8
FINE PRESHEAVES 329
9 APPLICATIONS OF THE COHOMOLOGY OF PRESHEAVES 338
1
CHARACTERISTIC CLASSES 346
EXERCISES 356
HOMOTOPY THEORY 38
2
1
EXACT SEQUENCES OF SETS OF HOMOTOPY CLASSES 364
2
HIGHER HOMOTOPY GROUPS 371 YY
3
CHANGE OF BASE POINTS 379
4
THE HUREWICZ HOMOMORPHISM 387
5
THE HUREWICZ ISOMORPHISM THEOREM 393
6
CW COMPLEXES 400
7
HOMOTOPY FUNCTORS 406
8
WEAK HOMOTOPY TYPE 412
EXERCISES 418
XIV
CONTENTS
8 OBSTRUCTION THEORY 42
2
1
EILENBERG-MACLANE SPACES 424
2
PRINCIPAL FIBRATIONS 432
3
MOORE-POSTNIKOV FACTORIZATIONS 437
4
OBSTRUCTION THEORY 445
5
THE SUSPENSION MAP 452
EXERCISES 460
9
SPECTRAL SEQUENCES AND HOMOTOPY
GROUPS OF SPHERES 46
4
1
SPECTRAL SEQUENCES 466
2
THE SPECTRAL SEQUENCE OF A FIBRATION 473
3
APPLICATIONS OF THE HOMOLOGY SPECTRAL SEQUENCE 481
4
MULTIPLICATIVE PROPERTIES OF SPECTRAL SEQUENCES- 490
5
APPLICATIONS OF THE COHOMOLOGY SPECTRAL SEQUENCE 498
S
SERRE CLASSES OF ABELIAN GROUPS 504
7
HOMOTOPY GROUPS OF SPHERES 512
EXERCISES 518
INDEX 52
1
|
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| author | Spanier, Edwin Henry 1921-1996 |
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| author_variant | e h s eh ehs |
| building | Verbundindex |
| bvnumber | BV010040375 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612 |
| callnumber-search | QA612 |
| callnumber-sort | QA 3612 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 300 |
| classification_tum | MAT 550f |
| ctrlnum | (OCoLC)33051461 (DE-599)BVBBV010040375 |
| dewey-full | 514/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.2 |
| dewey-search | 514/.2 |
| dewey-sort | 3514 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. print. |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV010040375 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:45:25Z |
| institution | BVB |
| isbn | 3540906460 0387906460 0387944265 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006658938 |
| oclc_num | 33051461 |
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| owner_facet | DE-29T DE-20 DE-384 DE-634 DE-83 |
| physical | XIV, 528 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Springer |
| record_format | marc |
| spelling | Spanier, Edwin Henry 1921-1996 Verfasser (DE-588)11565819X aut Algebraic topology Edwin H. Spanier 2. print. New York u.a. Springer 1989 XIV, 528 S. txt rdacontent n rdamedia nc rdacarrier Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Algebraische Topologie (DE-588)4120861-4 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006658938&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Spanier, Edwin Henry 1921-1996 Algebraic topology Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4120861-4 (DE-588)4123623-3 |
| title | Algebraic topology |
| title_auth | Algebraic topology |
| title_exact_search | Algebraic topology |
| title_full | Algebraic topology Edwin H. Spanier |
| title_fullStr | Algebraic topology Edwin H. Spanier |
| title_full_unstemmed | Algebraic topology Edwin H. Spanier |
| title_short | Algebraic topology |
| title_sort | algebraic topology |
| topic | Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Algebraic topology Algebraische Topologie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006658938&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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