Nilpotence and periodicity in stable homotopy theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, New Jersey
Princeton University Press
1992
|
| Series: | Annals of mathematics studies
number 128 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiv, 209 Seiten Illustrationen, Diagramme |
| ISBN: | 9780691025728 069108792X 069102572X |
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MARC
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| 245 | 1 | 0 | |a Nilpotence and periodicity in stable homotopy theory |c by Douglas C. Ravenel |
| 264 | 1 | |a Princeton, New Jersey |b Princeton University Press |c 1992 | |
| 264 | 4 | |c © 1992 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xi
Introduction xiii
1 The main theorems 1
1.1 Homotopy 1
1.2 Functors 2
1.3 Suspension 4
1.4 Self maps and the nilpotence theorem 6
1.5 Morava K theories and the periodicity theorem 6
2 Homotopy groups and the chromatic filtration 11
2.1 The definition of homotopy groups 11
2.2 Classical theorems 12
2.3 Cofibres 14
2.4 Motivating examples 16
2.5 The chromatic filtration 20
3 MU theory and formal group laws 25
3.1 Complex bordism 25
3.2 Formal group laws 26
3.3 The category Cr 29
3.4 Thick subcategories 33
4 Morava s orbit picture and Morava stabilizer groups 37
4.1 The action of F on L 37
4.2 Morava stabilizer groups 39
4.3 Cohomological properties of Sn 41
5 The thick subcategory theorem 45
5.1 Spectra 45
5.2 Spanier Whitehead duality 48
vii
5.3 The proof of the thick subcategory theorem 51
6 The periodicity theorem 53
6.1 Properties of vn maps 54
6.2 The Steenrod algebra and Margolis homology groups .... 58
6.3 The Adams spectral sequence and the un map on Y .... 61
6.4 The Smith construction 67
7 Bousfield localization and equivalence 69
7.1 Basic definitions and examples 69
7.2 Bousfield equivalence 72
7.3 The structure of (MU) 75
7.4 Some classes bigger than (MU) 76
7.5 £ (n) localization and the chromatic filtration 77
8 The proofs of the localization, smash product and chro¬
matic convergence theorems 81
8.1 LnBP and the localization theorem 82
8.2 Reducing the smash product theorem to a special example . 84
8.3 Constructing a finite torsion free prenilpotent spectrum . . 86
8.4 Some cohomological properties of profinite groups 90
8.5 The action of Sm on FK(m),(CP°°) 92
8.6 Chromatic convergence 95
9 The proof of the nilpotence theorem 99
9.1 The spectra X(n) 100
9.2 The proofs of the first two lemmas 102
9.3 A paradigm for proving the third lemma 106
9.4 The Snaith splitting of fi2S2m+1 108
9.5 The proof of the third lemma Ill
9.6 Historical note: theorems of Nishida and Toda 115
A Some tools from homotopy theory 119
A.I CW complexes 119
A.2 Loop spaces and spectra 122
A.3 Generalized homology and cohomology theories 126
A.4 Brown representability 1 ™
A.5 Limits in the stable homotopy category 131
A.6 The Adams spectral sequence 138
viii
B Complex bordism and SP theory 145
B.I Vector bundles and Thorn spectra 145
B.2 The Pontrjagin Thom construction 152
B.3 Hopf algebroids 154
B.4 The structure of MU,{MU) 159
B.5 5P theory 166
B.6 The Landweber exact functor theorem 172
B.7 Morava K theories 175
B.8 The change of rings isomorphism and the chromatic spectral
sequence 178
C Some idempotents associated with the symmetric group 183
C.I Constructing the idempotents 183
C.2 Idempotents for graded vector spaces 187
C.3 Getting strongly type n spectra from partially type n spectra 190
Bibliography 195
Index 205
ix
|
| any_adam_object | 1 |
| author | Ravenel, Douglas C. 1947- |
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| dewey-full | 514/.24 |
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| 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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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:57:57Z |
| institution | BVB |
| isbn | 9780691025728 069108792X 069102572X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004626879 |
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| physical | xiv, 209 Seiten Illustrationen, Diagramme |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spelling | Ravenel, Douglas C. 1947- Verfasser (DE-588)1237728789 aut Nilpotence and periodicity in stable homotopy theory by Douglas C. Ravenel Princeton, New Jersey Princeton University Press 1992 © 1992 xiv, 209 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies number 128 Homotopie gtt Homotopie ram Homotopy theory Stabile Homotopiegruppe (DE-588)4234506-6 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 s DE-604 Stabile Homotopiegruppe (DE-588)4234506-6 s Erscheint auch als Online-Ausgabe 978-1-4008-8248-9 Annals of mathematics studies number 128 (DE-604)BV000000991 128 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004626879&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ravenel, Douglas C. 1947- Nilpotence and periodicity in stable homotopy theory Annals of mathematics studies Homotopie gtt Homotopie ram Homotopy theory Stabile Homotopiegruppe (DE-588)4234506-6 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4234506-6 (DE-588)4128142-1 |
| title | Nilpotence and periodicity in stable homotopy theory |
| title_auth | Nilpotence and periodicity in stable homotopy theory |
| title_exact_search | Nilpotence and periodicity in stable homotopy theory |
| title_full | Nilpotence and periodicity in stable homotopy theory by Douglas C. Ravenel |
| title_fullStr | Nilpotence and periodicity in stable homotopy theory by Douglas C. Ravenel |
| title_full_unstemmed | Nilpotence and periodicity in stable homotopy theory by Douglas C. Ravenel |
| title_short | Nilpotence and periodicity in stable homotopy theory |
| title_sort | nilpotence and periodicity in stable homotopy theory |
| topic | Homotopie gtt Homotopie ram Homotopy theory Stabile Homotopiegruppe (DE-588)4234506-6 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Homotopie Homotopy theory Stabile Homotopiegruppe Homotopietheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004626879&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT raveneldouglasc nilpotenceandperiodicityinstablehomotopytheory |