Fibrewise homotopy theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
1998
|
| Series: | Springer Monographs in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 341 S. |
| ISBN: | 1852330147 |
Staff View
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| 245 | 1 | 0 | |a Fibrewise homotopy theory |c Michael Crabb ; Ioan James |
| 264 | 1 | |a London [u.a.] |b Springer |c 1998 | |
| 300 | |a VIII, 341 S. | ||
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| 650 | 7 | |a Compactification Aleksandrov |2 Jussieu | |
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| 650 | 7 | |a Fibration Hopf |2 Jussieu | |
| 650 | 7 | |a Homologue fibrée |2 Jussieu | |
| 650 | 7 | |a Homotopie |2 ram | |
| 650 | 7 | |a Point fixe |2 Jussieu | |
| 650 | 4 | |a Fiber bundles (Mathematics) | |
| 650 | 4 | |a Homotopy theory | |
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Record in the Search Index
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|---|---|
| adam_text |
Contents
Part I. A Survey of Fibrewise Homotopy Theory
Introduction 1
Chapter 1: An Introduction to Fibrewise Homotopy Theory
1. Fibrewise spaces 3
2. Fibrewise transformation groups 13
3. Fibrewise homotopy 21
4. Fibrewise cofibrations 24
5. Fibrewise fibrations 26
6. Numerable coverings 31
7. Fibrewise fibre bundles 34
8. Fibrewise mapping spaces 40
Chapter 2: The Pointed Theory
9. Fibrewise pointed spaces 53
10. Fibrewise one point (Alexandroff) compactification 57
11. Fibrewise pointed homotopy 60
12. Fibrewise pointed cofibrations 65
13. Fibrewise pointed fibrations 69
14. Numerable coverings (continued) 75
15. Fibrewise pointed mapping spaces 77
16. Fibrewise well pointed and fibrewise non degenerate spaces 82
17. Fibrewise complexes 87
18. Fibrewise Whitehead products 94
Chapter 3: Applications
19. Numerical invariants 101
20. The reduced product (James) construction Ill
21. Fibrewise Hopf and coHopf structures 115
22. Fibrewise manifolds 126
23. Fibrewise configuration spaces 129
viii Contents
Part II. An Introduction to Fibrewise Stable Homotopy Theory
Introduction 137
Chapter 1: Foundations
1. Fibre bundles 141
2. Complements on homotopy theory 155
3. Stable homotopy theory 167
4. The Euler class 178
Chapter 2: Fixed point Methods
5. Fibrewise Euclidean and Absolute Neighbourhood
Retracts 187
6. Lefschetz fixed point theory for fibrewise ENRs 201
7. Fixed point theory for fibrewise ANRs 212
8. Virtual vector bundles and stable spaces 219
9. The Adams conjecture 225
10. Duality 232
Chapter 3: Manifold Theory
11. Fibrewise differential topology 243
12. The Pontrjagin Thom construction 258
13. Miller's stable splitting of U{n) 285
14. Configuration spaces and splittings 291
Chapter 4: Homology Theory
15. Fibrewise homology 309
References 331
Index 337 |
| any_adam_object | 1 |
| author | Crabb, Michael C. 1949- James, Ioan M. 1928-2025 |
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| callnumber-raw | QA612.7 |
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| callnumber-sort | QA 3612.7 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 300 SK 350 |
| ctrlnum | (OCoLC)38908611 (DE-599)BVBBV012119010 |
| dewey-full | 514/.24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.24 |
| dewey-search | 514/.24 |
| dewey-sort | 3514 224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012119010 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-26T05:00:09Z |
| institution | BVB |
| isbn | 1852330147 |
| language | English |
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| physical | VIII, 341 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
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| series2 | Springer Monographs in mathematics |
| spelling | Crabb, Michael C. 1949- Verfasser (DE-588)120071258 aut Fibrewise homotopy theory Michael Crabb ; Ioan James London [u.a.] Springer 1998 VIII, 341 S. txt rdacontent n rdamedia nc rdacarrier Springer Monographs in mathematics Compactification Aleksandrov Jussieu Espace fibré Jussieu Faisceaux fibrés (Mathématiques) ram Fibration Hopf Jussieu Homologue fibrée Jussieu Homotopie ram Point fixe Jussieu Fiber bundles (Mathematics) Homotopy theory Faserbündel (DE-588)4135582-9 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 s Faserbündel (DE-588)4135582-9 s DE-604 James, Ioan M. 1928-2025 Verfasser (DE-588)119539888 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008206973&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Crabb, Michael C. 1949- James, Ioan M. 1928-2025 Fibrewise homotopy theory Compactification Aleksandrov Jussieu Espace fibré Jussieu Faisceaux fibrés (Mathématiques) ram Fibration Hopf Jussieu Homologue fibrée Jussieu Homotopie ram Point fixe Jussieu Fiber bundles (Mathematics) Homotopy theory Faserbündel (DE-588)4135582-9 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4135582-9 (DE-588)4128142-1 |
| title | Fibrewise homotopy theory |
| title_auth | Fibrewise homotopy theory |
| title_exact_search | Fibrewise homotopy theory |
| title_full | Fibrewise homotopy theory Michael Crabb ; Ioan James |
| title_fullStr | Fibrewise homotopy theory Michael Crabb ; Ioan James |
| title_full_unstemmed | Fibrewise homotopy theory Michael Crabb ; Ioan James |
| title_short | Fibrewise homotopy theory |
| title_sort | fibrewise homotopy theory |
| topic | Compactification Aleksandrov Jussieu Espace fibré Jussieu Faisceaux fibrés (Mathématiques) ram Fibration Hopf Jussieu Homologue fibrée Jussieu Homotopie ram Point fixe Jussieu Fiber bundles (Mathematics) Homotopy theory Faserbündel (DE-588)4135582-9 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Compactification Aleksandrov Espace fibré Faisceaux fibrés (Mathématiques) Fibration Hopf Homologue fibrée Homotopie Point fixe Fiber bundles (Mathematics) Homotopy theory Faserbündel Homotopietheorie |
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