Obstruction theory on homotopy classification of maps:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York
Springer-Verlag
1977
|
| Series: | Lecture notes in mathematics
628 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 387 Seiten Diagramme |
| ISBN: | 3540085343 0387085343 |
Staff View
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| 245 | 1 | 0 | |a Obstruction theory on homotopy classification of maps |c Hans J. Baues |
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Record in the Search Index
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|---|---|
| adam_text | Contents
CHAPTER 0. CONVENTIONS AND NOTATION
(0.0) Maps and homotopy, and excision theorems 1
(0.1) Cofibrations and fibrations 15
(0.2) Homotopy groups 23
(0.3) Whitehead products 26
(0.4) Operation of the fundamental group 29
(0.5) Homology and cohomology groups 32
CHAPTER 1. PRINCIPAL FIBRATIONS AND COFIBRATIONS,
OBSTRUCTIONS AND DIFFERENCES
(1.1) Extension and lifting problems 35
(1.2) Principal cofibrations and extension of maps and
sections 46
(1.3) Principal fibrations and lifting of maps and
retractions 68
(1.4) CW-spaces 94
(1.5) Postnikov spaces 110
CHAPTER 2. RELATIVE PRINCIPAL COFIBRATIONS AND FIBRATIONS
(2.1) Relative principal cofibrations 121
(2.2) Relative principal fibrations 131
(2.3) Postnikov decompositions, CW-decompositions, and
their principal reductions 141
(2.4) The exact classification sequences of a principal
cofibration 151
Example: Classification of maps from an n-dimen -
sional Torus into the 2-sphere 159
VI
(2.5) The exact classification sequences of a principal
fibration 161
(2.6) The fiber and cofiber sequences in the category
of ex-spaces 166
CHAPTER 3. ITERATED PRINCIPAL COFIBRATIONS
(3.1) The partial suspension 171
Appendix: The algebra of stable and partially stable
maps and the Pontrjagin algebra 177
(3.2) The classification of maps and sections by means of
iterated principal cofibrations and the associated
spectral sequence 183
Appendix: Iterated principal cofibrations and the
associated chain complex 194
(3.3) The first differential of the spectral sequence,
Whitehead products and relative Whltehead products 197
Appendix: Classification of fibrations over a
suspension, twisting maps 208
(3.4) The functional suspension. Some general suspension
theorems 213
(3.5) Functional suspension and the principal reduction 220
Appendix: The principal reduction of a CW-decompo-
sition 228
(3.6) Examples of secondary homotopy classification,
Toda brackets, triple Whitehead-products, and
secondary obstructions in complex projective spaces 231
VII
CHAPTER 4. OBSTRUCTION THEORY FOR CW-COMPLEXES
(4.1) Cohomology with local coefficients 242
Appendix: Examples of local qroups 249
(4.2) The obstruction cocycle and the difference cochain . 254
(4.3) 2-extendability of a section. Primary cohomology
obstructions 265
(4.4) The spectral sequence for the classifying
maps and sections on CW-complexes 276
CHAPTER 5. POSTNIKOV HOMOTOPY DECOMPOSITIONS
(5.1) Difference fibrations 293
(5.2) Classification of fibrations with fiber an
Eilenberg-Mac Lane space 298
Appendix: The classifying space for fibrations with
fiber an Eilenberg-Mac Lane space 305
(5.3) Postnikov decompositions 306
Appendix: Principal approximation of
K(G, n) - fibrations 312
(5.4) Cohomology obstructions of higher order 315
CHAPTER 6. ITERATED PRINCIPAL FIBRATIONS
(6.1) The partial loop operation 324
Appendix: The algebra of stable and patially stable
cohomology operations, the Steenrod algebra and the
Massey- Peterson algebra 330
VIII
(6.2) Iterated principal fibrations and the derived
spectral sequence for the classification of maps and
retractions 334
Appendix: Iterated principal fibrations and the
associated chain complex 340
(6.3) The first differential of the spectral sequence,
cup-products and relative cup-products 342
(6.4) The functional loop operation 349
(6.5) The functional loop operation and the principal
reduction of fibrations 354
Appendix: The principal reduction of a Postnikov
decompos ition 357
(6.6) Examples of secondary homotopy classification.
Triple Massey products. The classification of vector
bundles 358
List of svnhols 368
References 370
Index 379
|
| any_adam_object | 1 |
| author | Baues, Hans J. 1943- |
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| author_facet | Baues, Hans J. 1943- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV002252300 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:48Z |
| institution | BVB |
| isbn | 3540085343 0387085343 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001480023 |
| oclc_num | 252328250 |
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| physical | XI, 387 Seiten Diagramme |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Springer-Verlag |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Baues, Hans J. 1943- (DE-588)128430702 aut Obstruction theory on homotopy classification of maps Hans J. Baues Berlin ; Heidelberg ; New York Springer-Verlag 1977 XI, 387 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 628 Applications (Mathématiques) Homotopie Obstructions, Théorie des Homotopy theory Mappings (Mathematics) Obstruction theory Hindernistheorie (DE-588)4159903-2 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 s Hindernistheorie (DE-588)4159903-2 s DE-604 Erscheint auch als Online-Ausgabe 978-3-540-08534-8 Lecture notes in mathematics 628 (DE-604)BV000676446 628 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001480023&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baues, Hans J. 1943- Obstruction theory on homotopy classification of maps Lecture notes in mathematics Applications (Mathématiques) Homotopie Obstructions, Théorie des Homotopy theory Mappings (Mathematics) Obstruction theory Hindernistheorie (DE-588)4159903-2 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4159903-2 (DE-588)4120861-4 |
| title | Obstruction theory on homotopy classification of maps |
| title_auth | Obstruction theory on homotopy classification of maps |
| title_exact_search | Obstruction theory on homotopy classification of maps |
| title_full | Obstruction theory on homotopy classification of maps Hans J. Baues |
| title_fullStr | Obstruction theory on homotopy classification of maps Hans J. Baues |
| title_full_unstemmed | Obstruction theory on homotopy classification of maps Hans J. Baues |
| title_short | Obstruction theory on homotopy classification of maps |
| title_sort | obstruction theory on homotopy classification of maps |
| topic | Applications (Mathématiques) Homotopie Obstructions, Théorie des Homotopy theory Mappings (Mathematics) Obstruction theory Hindernistheorie (DE-588)4159903-2 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Applications (Mathématiques) Homotopie Obstructions, Théorie des Homotopy theory Mappings (Mathematics) Obstruction theory Hindernistheorie Algebraische Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001480023&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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