Spectra and the Steenrod algebra: modules over the Steenrod algebra and the stable homotopy category
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam, [u.a.]
North-Holland
1983
|
| Series: | North-Holland Mathematical Library
Volume 29 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xix, 489 Seiten |
| ISBN: | 0444865160 |
Staff View
MARC
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| 100 | 1 | |a Margolis, Harvey R. |4 aut | |
| 245 | 1 | 0 | |a Spectra and the Steenrod algebra |b modules over the Steenrod algebra and the stable homotopy category |c H. R. Margolis |
| 264 | 1 | |a Amsterdam, [u.a.] |b North-Holland |c 1983 | |
| 300 | |a xix, 489 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a North-Holland Mathematical Library |v Volume 29 | |
| 650 | 4 | |a Catégories (Mathématiques) | |
| 650 | 4 | |a Modules (Algèbre) | |
| 650 | 4 | |a Spectre (Mathématiques) | |
| 650 | 4 | |a Steenrod, Algèbre de | |
| 650 | 7 | |a Topologia Algebrica |2 larpcal | |
| 650 | 4 | |a Categories (Mathematics) | |
| 650 | 4 | |a Modules (Algebra) | |
| 650 | 4 | |a Spectral theory (Mathematics) | |
| 650 | 4 | |a Steenrod algebra | |
| 650 | 0 | 7 | |a Kategorientheorie |0 (DE-588)4120552-2 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text |
CONTENTS
Introduction v
Part I: The Stable Homotopy Category
Chapter 1: Stable Homotopy Theory and the Spanier Whitehead
Category 3
§1. Stable Homotopy Theory 3
§2. The Spanier Whitehead Category 6
Chapter 2. Stable Homotopy Categories 20
§1. The Axioms 20
§2. A Model for the Axioms 27
Chapter 3. Colimit Structures 33
§1. Weak Colimits in .9 33
§2. Some Applications 38
Chapter 4. Homology and Cohomology Functors 45
§1. Basic Properties of Homology and Cohomology Functors 45
§2. Finitely Determined Functors 49
§3. Representability Theorems 59
Chapter 5. Applications of Homology and Cohomology Functors 64
§1. Function and Dual Spectra 64
§2. Limit Structures 70
§3. Applications to Foundations 74
Chapter 6. G Homology and G Cohomology 85
§1. Eilenberg MacLane Spectra 85
§2. HG» and HG* 87
S3. The Cellular Tower 92
Chapter 7. Localization 101
Chapter 8. .^ Localization 109
§1. Localization and Local Spectra 110
§2. The Relationship Between a Spectrum and its Localization 125
xvi
Contents xvii
Chapter 9. ^ Completion 128
§1. Completion Constructions 129
§2. Categories of Complete Spectra 143
Chapter 10. Unique Factorization, Genus and Cancellation 152
§1. Unique Factorization Theorems 152
§2. Application to the Structure of Finite Spectra 160
Part II: The Steenrod Algebra and Spectra: Surface
Structure
Chapter 11. Modules over Connected Algebras 169
§1. Basic Definitions 169
§2. The Projective Cover and Bounded Below Modules 172
§3. Structure in the Module Categories 176
§4. The Unique Decomposition Theorem 181
Chapter 12. Modules over Hopf Algebras 185
§1. Hopf Algebras 185
§2. Finite Hopf Algebras 188
Chapter 13. Modules over P Algebras 192
§1. Definition and Basic Properties 192
§2. The Unbounded Case 196
§3. The Bounded Below Case 199
Chapter 14. The Stable Category of Modules 204
§1. The Stable Category of Modules 205
§2. The Stable Structure of Bounded Below Modules 216
§3. The Loop Functor 222
Chapter 15. The Mod p Steenrod Algebra and Modules over It 227
§1. The Mod 2 Steenrod Algebra 227
§2. Modules over the Mod p Steenrod Algebra 240
§3. Doubling 247
xviii Contents
Chapter 16. Zp Cohomology and the Steenrod Algebra 249
§1. Zp Cohomology and the Steenrod Algebra 250
§2. Some Elementary Applications 261
§3. Higher Operations and Realizability 266
§4. The Adams Spectral Sequence 273
Chapter 17. The Stable Category of Spectra 279
§1. The Structure of the Stable Category of Spectra 280
§2. Relation to Other Structure 292
§3. Secondary Phenomena 297
Part III: The Steenrod Algebra and Spectra: Deep
Structure
Chapter 18. Modules over Exterior Algebras 313
§1. The Homology Groups 314
§2. Modules over E[ei, e^\ 316
§3. The Whitehead Theorem 320
§4. Killing the Homology Groups 321
§5. The Periodicity Problem 327
Chapter 19. The PJ Homology Groups of Modules 330
§1. The Homology Groups of A Modules 331
§2. The Whitehead Theorem 335
§3. The Homology Groups and Structure in AM 340
§4. The Homology Groups of Extended Modules 344
Chapter 20. The P? Cohomology Groups of Spectra 352
§1. The P? Cohomology Groups of Spectra 352
§2. The P? Cohomology Groups 359
Chapter 21. Killing the Pf GROUPS 371
§1. The Killing Constructions 372
§2. Proof of the Existence Theorem 377
Chapter 22. Modules and Spectra with PJ Groups Killed 388
§1. Complementarity 389
§2. Convergence 390
§3. Connectivity 398
§4. Complexity 401
Contents xix
Chapter 23. Modules and Spectra with One Non Vanishing P',
Group 407
§1. PJ Local Objects 407
§2. i^ Local Objects 410
§3. Periodicity 413
Chapter 24. Applications of the PJ Groups 425
§1. Applications to the Adams Spectral Sequence 425
§2. Application to Localization 430
§3. Application to Bordism 434
Appendices
Appendix 1. Categories and Limit Structures 439
§1. General Notions 439
§2. Limit Structures 443
§3. Categories of Fractions 450
Appendix 2. Triangulated Categories 453
Appendix 3. Localization and Completion of Abelian Groups 471
§1. Localization 471
§2. Completion 474
Bibliography 480
Symbol List 485
Index 487 |
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| author | Margolis, Harvey R. |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV000230452 |
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| institution | BVB |
| isbn | 0444865160 |
| language | English |
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| spelling | Margolis, Harvey R. aut Spectra and the Steenrod algebra modules over the Steenrod algebra and the stable homotopy category H. R. Margolis Amsterdam, [u.a.] North-Holland 1983 xix, 489 Seiten txt rdacontent n rdamedia nc rdacarrier North-Holland Mathematical Library Volume 29 Catégories (Mathématiques) Modules (Algèbre) Spectre (Mathématiques) Steenrod, Algèbre de Topologia Algebrica larpcal Categories (Mathematics) Modules (Algebra) Spectral theory (Mathematics) Steenrod algebra Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Steenrod-Algebra (DE-588)4182999-2 gnd rswk-swf Modul (DE-588)4129770-2 gnd rswk-swf Modul (DE-588)4129770-2 s Kategorientheorie (DE-588)4120552-2 s DE-604 Spektraltheorie (DE-588)4116561-5 s Steenrod-Algebra (DE-588)4182999-2 s North-Holland Mathematical Library Volume 29 (DE-604)BV000005206 29 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000138081&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Margolis, Harvey R. Spectra and the Steenrod algebra modules over the Steenrod algebra and the stable homotopy category North-Holland Mathematical Library Catégories (Mathématiques) Modules (Algèbre) Spectre (Mathématiques) Steenrod, Algèbre de Topologia Algebrica larpcal Categories (Mathematics) Modules (Algebra) Spectral theory (Mathematics) Steenrod algebra Kategorientheorie (DE-588)4120552-2 gnd Spektraltheorie (DE-588)4116561-5 gnd Steenrod-Algebra (DE-588)4182999-2 gnd Modul (DE-588)4129770-2 gnd |
| subject_GND | (DE-588)4120552-2 (DE-588)4116561-5 (DE-588)4182999-2 (DE-588)4129770-2 |
| title | Spectra and the Steenrod algebra modules over the Steenrod algebra and the stable homotopy category |
| title_auth | Spectra and the Steenrod algebra modules over the Steenrod algebra and the stable homotopy category |
| title_exact_search | Spectra and the Steenrod algebra modules over the Steenrod algebra and the stable homotopy category |
| title_full | Spectra and the Steenrod algebra modules over the Steenrod algebra and the stable homotopy category H. R. Margolis |
| title_fullStr | Spectra and the Steenrod algebra modules over the Steenrod algebra and the stable homotopy category H. R. Margolis |
| title_full_unstemmed | Spectra and the Steenrod algebra modules over the Steenrod algebra and the stable homotopy category H. R. Margolis |
| title_short | Spectra and the Steenrod algebra |
| title_sort | spectra and the steenrod algebra modules over the steenrod algebra and the stable homotopy category |
| title_sub | modules over the Steenrod algebra and the stable homotopy category |
| topic | Catégories (Mathématiques) Modules (Algèbre) Spectre (Mathématiques) Steenrod, Algèbre de Topologia Algebrica larpcal Categories (Mathematics) Modules (Algebra) Spectral theory (Mathematics) Steenrod algebra Kategorientheorie (DE-588)4120552-2 gnd Spektraltheorie (DE-588)4116561-5 gnd Steenrod-Algebra (DE-588)4182999-2 gnd Modul (DE-588)4129770-2 gnd |
| topic_facet | Catégories (Mathématiques) Modules (Algèbre) Spectre (Mathématiques) Steenrod, Algèbre de Topologia Algebrica Categories (Mathematics) Modules (Algebra) Spectral theory (Mathematics) Steenrod algebra Kategorientheorie Spektraltheorie Steenrod-Algebra Modul |
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