Rings, modules, and algebras in stable homotopy theory:
Gespeichert in:
| Beteiligte Personen: | , , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[1997]
|
| Schriftenreihe: | Mathematical surveys and monographs
Volume 47 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007489404&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xi, 249 Seiten Illustrationen, Diagramme |
| ISBN: | 0821806386 9780821843031 |
Internformat
MARC
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| 100 | 1 | |a Elmendorf, Anthony D. |d 1952- |e Verfasser |0 (DE-588)173033504 |4 aut | |
| 245 | 1 | 0 | |a Rings, modules, and algebras in stable homotopy theory |c A. D. Elmendorf, I. Kriz, M.A. Mandell, J. P. May. With an appendix by M. Cole |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [1997] | |
| 264 | 4 | |c © 1997 | |
| 300 | |a xi, 249 Seiten |b Illustrationen, Diagramme | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Mathematical surveys and monographs |v Volume 47 | |
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| 650 | 4 | |a Point set theory | |
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| 700 | 1 | |a Kriz, Igor |e Verfasser |0 (DE-588)1043711279 |4 aut | |
| 700 | 1 | |a Mandell, M. A. |d 1970- |e Verfasser |0 (DE-588)173564429 |4 aut | |
| 700 | 1 | |a May, Jon Peter |d 1939- |e Verfasser |0 (DE-588)122391810 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1819377482850107392 |
|---|---|
| adam_text | Contents
Introduction 1
Chapter I. Prologue: the category of L spectra 9
1. Background on spectra and the stable homotopy category 9
2. External smash products and twisted half smash products 11
3. The linear isometries operad and internal smash products 13
4. The category of L spectra 17
5. The smash product of L spectra 20
6. The equivalence of the old and new smash products 22
7. Function L spectra 25
8. Unital properties of the smash product of L spectra 28
Chapter II. Structured ring and module spectra 31
1. The category of S modules 31
2. The mirror image to the category of S modules 35
3. S algebras and their modules 37
4. Free A^ and E^ ring spectra; comparisons of definitions 39
5. Free modules over Aoa and Ex ring spectra 42
6. Composites of monads and monadic tensor products 44
7. Limits and colimits of S algebras 47
Chapter III. The homotopy theory of .R modules 51
1. The category of .R modules; free and cofree R modules 51
2. Cell and CW .R modules; the derived category of .R modules 54
3. The smash product of .R modules 58
4. Change of S algebras; g cofibrant S algebras 61
5. Symmetric and extended powers of .R modules 64
6. Function .R modules 65
7. Commutative S algebras and duality theory 69
Chapter IV. The algebraic theory of il modules 71
1. Tor and Ext; homology and cohomology; duality 71
2. Eilenberg Mac Lane spectra and derived categories 74
3. The Atiyah Hirzebruch spectral sequence 78
4. Universal coefficient and Kunneth spectral sequences 81
5. The construction of the spectral sequences 83
6. Eilenberg Moore type spectral sequences 86
7. The bar constructions B(M, R, N) and B(X, G, Y) 88
ix
x CONTENTS
Chapter V. .R ring spectra and the specialization to MU 91
1. Quotients by ideals and localizations 91
2. Localizations and quotients of .R ring spectra 95
3. The associativity and commutativity of .R ring spectra 98
4. The specialization to MCZ modules and algebras 101
Chapter VI. Algebraic K theory of S algebras 103
1. Waldhausen categories and algebraic /f theory 103
2. Cylinders, homotopies, and approximation theorems 106
3. Application to categories of /^ modules 110
4. Homotopy invariance and Quillen s algebraic if theory of rings 113
5. Morita equivalence 115
6. Multiplicative structure in the commutative case 119
7. The plus construction description of KR 121
8. Comparison with Waldhausen s K theory of spaces 125
Chapter VII. .R algebras and topological model categories 127
1. .R algebras and their modules 128
2. Tensored and cotensored categories of structured spectra 130
3. Geometric realization and calculations of tensors 135
4. Model categories of ring, module, and algebra spectra 140
5. The proofs of the model structure theorems 144
6. The underlying H modules of g cofibrant .R algebras 148
7. g cofibrations and weak equivalences; cofibrations 151
Chapter VIII. Bousfield localizations of .R modules and algebras 155
1. Bousfield localizations of R modules 155
2. Bousfield localizations of .R algebras 159
3. Categories of local modules 163
4. Periodicity and /{ theory 165
Chapter IX. Topological Hochschild homology and cohomology 167
1. Topological Hochschild homology: first definition 168
2. Topological Hochschild homology: second definition 172
3. The isomorphism between thhR(A) and A g Sl 176
Chapter X. Some basic constructions on spectra 179
1. The geometric realization of simplicial spectra 179
2. Homotopical and homological properties of realization 182
3. Homotopy colimits and limits 186
4. E cofibrant, LEC, and CW prespectra 188
5. The cylinder construction 191
Chapter XI. Spaces of linear isometries and technical theorems 197
1. Spaces of linear isometries 197
2. Fine structure of the linear isometries operad 200
3. The unit equivalence for the operadic smash product 205
CONTENTS x
Chapter XII. The monadic bar construction 209
1. The bar construction and two deferred proofs 209
2. Cofibrations and the bar construction 211
Chapter XIII. Epilogue: The category of L spectra under 5 215
1. The modified smash products y, s , and * 215
2. The modified smash products r,0r, and *r 219
Appendix A. Twisted half smash products and function spectra 225
1. Introduction 225
2. The category S*(U ; U) 226
3. Smash products and function spectra 227
4. The object Jta € y(U ; U) 229
5. Twisted half smash products and function spectra 231
6. Formal properties of twisted half smash products 234
7. Homotopical properties of a x E and F[a, E ) 237
8. The cofibration theorem 239
9. Equivariant twisted half smash products 241
Bibliography 243
Index 247
|
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| id | DE-604.BV011170946 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:07:32Z |
| institution | BVB |
| isbn | 0821806386 9780821843031 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007489404 |
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| owner_facet | DE-12 DE-355 DE-BY-UBR DE-824 DE-384 DE-11 DE-188 DE-19 DE-BY-UBM |
| physical | xi, 249 Seiten Illustrationen, Diagramme |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spellingShingle | Elmendorf, Anthony D. 1952- Kriz, Igor Mandell, M. A. 1970- May, Jon Peter 1939- Rings, modules, and algebras in stable homotopy theory Mathematical surveys and monographs Homotopie ram Homotopy theory Point set theory Homotopie (DE-588)4025803-8 gnd Punktgruppe (DE-588)4176373-7 gnd |
| subject_GND | (DE-588)4025803-8 (DE-588)4176373-7 |
| title | Rings, modules, and algebras in stable homotopy theory |
| title_auth | Rings, modules, and algebras in stable homotopy theory |
| title_exact_search | Rings, modules, and algebras in stable homotopy theory |
| title_full | Rings, modules, and algebras in stable homotopy theory A. D. Elmendorf, I. Kriz, M.A. Mandell, J. P. May. With an appendix by M. Cole |
| title_fullStr | Rings, modules, and algebras in stable homotopy theory A. D. Elmendorf, I. Kriz, M.A. Mandell, J. P. May. With an appendix by M. Cole |
| title_full_unstemmed | Rings, modules, and algebras in stable homotopy theory A. D. Elmendorf, I. Kriz, M.A. Mandell, J. P. May. With an appendix by M. Cole |
| title_short | Rings, modules, and algebras in stable homotopy theory |
| title_sort | rings modules and algebras in stable homotopy theory |
| topic | Homotopie ram Homotopy theory Point set theory Homotopie (DE-588)4025803-8 gnd Punktgruppe (DE-588)4176373-7 gnd |
| topic_facet | Homotopie Homotopy theory Point set theory Punktgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007489404&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
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