Equivariant homotopy and cohomology theory: dedicated to the memory of Robert J. Piacenza
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
1996
|
| Series: | Regional Conference Series in Mathematics
91 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 366 Seiten graph. Darst. |
| ISBN: | 0821803190 |
Staff View
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| 245 | 1 | 0 | |a Equivariant homotopy and cohomology theory |b dedicated to the memory of Robert J. Piacenza |c J. P. May ... |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 1996 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction 1
Chapter I. Equivariant cellular and homology theory 11
1. Some basic definitions and adjunctions 11
2. Analogues for based G spaces 12
3. G CW complexes . 13
4. Ordinary homology and cohomology theories 16
5. Obstruction theory 18
6. Universal coefficient spectral sequences 19
Chapter II. Postnikov systems, localization, and completion 21
1. Eilenberg Mac Lane G spaces and Postnikov systems 21
2. Summary: localizations of spaces 22
3. Localizations of G spaces 23
4. Summary: completions of spaces 24
5. Completions of G spaces 26
Chapter III. Equivariant rational homotopy theory (by Georgia
Triantafillou) 27
1. Summary: the theory of minimal models 27
2. Equivariant minimal models 29
3. Rational equivariant Hopf spaces 31
Chapter IV. Smith theory 33
1. Smith theory via Bredon cohomology 33
2. Borel cohomology, localization, and Smith theory 35
Chapter V. Categorical constructions; equivariant applications 39
1. Coends and geometric realization 39
2. Homotopy colimits and limits 41
3. Elmendorf s theorem on diagrams of fixed point spaces 43
4. Eilenberg Mac Lane G spaces and universal ^ spaces 45
Chapter VI. The homotopy theory of diagrams (by Robert J.
Piacenza) 47
1. Elementary homotopy theory of diagrams 47
2. Homotopy groups 49
3. Cellular theory 50
4. The homology and cohomology theory of diagrams 52
5. The closed model structure on %J 53
6. Another proof of Elmendorf s theorem 56
Chapter VII. Equivariant bundle theory and classifying spaces 59
1. The definition of equivariant bundles 59
2. The classification of equivariant bundles 60
3. Some examples of classifying spaces 62
x CONTENTS
Chapter VIII. The Sullivan conjecture 67
1. Statements of versions of the Sullivan conjecture 67
2. Algebraic preliminaries: Lannes functors T and Fix 70
3. Lannes generalization of the Sullivan conjecture 71
4. Sketch proof of Lannes theorem 73
5. Maps between classifying spaces 75
Chapter IX. An introduction to equivariant stable homotopy 79
1. G spheres in homotopy theory 79
2. G Universes and stable G maps 81
3. Euler characteristic and transfer G maps 83
4. Mackey functors and coMackey functors 84
5. J?0(G) graded homology and cohomology 86
6. The Conner conjecture 88
Chapter X. G CW(V) complexes and i2O(G) graded cohomology
(by Stefan Waner) 89
1. Motivation for cellular theories based on representations 89
2. G CW(F) complexes 90
3. Homotopy theory of G CW(F) complexes 92
4. Ordinary i?O(G) graded homology and cohomology 94
Chapter XI. The equivariant Hurewicz and suspension theorems
(by L. Guance Lewis, Jr.) 97
1. Background on the classical theorems 97
2. Formulation of the problem and counterexamples 98
3. An oversimplified description of the results 101
4. The statements of the theorems 103
5. Sketch proofs of the theorems 106
Chapter XII. The equivariant stable homotopy category 111
1. An introductory overview 111
2. Prespectra and spectra 113
3. Smash products 115
4. Function spectra 117
5. The equivariant case 119
6. Spheres and homotopy groups 119
7. G CW spectra 122
8. Stability of the stable category 125
9. Getting into the stable category 126
Chapter XIII. i?O(G) graded homology and cohomology theories 129
1. Axioms for i?O(G) graded cohomology theories 129
2. Representing i?O(G) graded theories by G spectra 131
3. Brown s theorem and i?O(G) graded cohomology 134
4. Equivariant Eilenberg Mac Lane spectra 136
5. Ring G spectra and products 139
Chapter XIV. An introduction to equivariant iiT theory (by
J. P. C. Greenlees) 143
1. The definition and basic properties of ife theory 143
2. Bundles over a point: the representation ring 144
3. Equivariant Bott periodicity 146
4. Equivariant if theory spectra 147
5. The Atiyah Segal completion theorem 149
CONTENTS xi
6. The generalization to families 151
Chapter XV. An introduction to equivariant cobordism (by S. R.
Costenoble) 153
1. A review of nonequivariant cobordism 153
2. Equivariant cobordism and Thorn spectra 155
3. Computations: the use of families 158
4. Special cases: odd order groups and Z/2 161
Chapter XVI. Spectra and G spectra; change of groups; duality 163
1. Fixed point spectra and orbit spectra 163
2. Split G spectra and free G spectra 165
3. Geometric fixed point spectra 166
4. Change of groups and the Wirthmiiller isomorphism 167
5. Quotient groups and the Adams isomorphism 169
6. The construction of G/TV spectra from G spectra 171
7. Spanier Whitehead duality 173
8. F duality of G spaces and Atiyah duality 175
9. Poincare duality 176
Chapter XVII. The Burnside ring 179
1. Generalized Euler characteristics and transfer maps 179
2. The Burnside ring A(G) and the zero stem ir^{S) 182
3. Prime ideals of the Burnside ring 183
4. Idempotent elements of the Burnside ring 185
5. Localizations of the Burnside ring 186
6. Localization of equivariant homology and cohomology 188
Chapter XVIII. Transfer maps in equivariant bundle theory 191
1. The transfer and a dimension shifting variant 191
2. Basic properties of transfer maps 193
3. Smash products and Euler characteristics 195
4. The double coset formula and its applications 197
5. Transitivity of the transfer 201
Chapter XIX. Stable homotopy and Mackey functors 203
1. The splitting of equivariant stable homotopy groups 203
2. Generalizations of the splitting theorems 206
3. Equivalent definitions of Mackey functors 207
4. Induction theorems 209
5. Splittings of rational G spectra for finite groups G 212
Chapter XX. The Segal conjecture 215
1. The statement in terms of completions of G spectra 215
2. A calculational reformulation 217
3. A generalization and the reduction to finite p groups 219
4. The proof of the Segal conjecture for finite p groups 221
5. Approximations of singular subspaces of G spaces 223
6. An inverse limit of Adams spectral sequences 225
7. Further generalizations; maps between classifying spaces 227
Chapter XXI. Generalized Tate cohomology (by J. P. C.
Greenlees and J. P. May) 231
1. Definitions and basic properties 231
2. Ordinary theories; Atiyah Hirzebruch spectral sequences 234
3. Cohomotopy, periodicity, and root invariants 236
xii CONTENTS
4. The generalization to families 237
5. Equivariant .KT theory 240
6. Further calculations and applications 242
Chapter XXII. Twisted half smash products and function spectra
(by Michael Cole) 247
1. Introduction 247
2. The category GS{U ; U) 250
3. Smash products and function spectra 251
4. The object JCa € G S(U ; U) 252
5. Twisted half smash products and function spectra 255
6. Homotopicalproperties ofaKE and F[a,E ) 257
Chapter XXIII. Brave new algebra 261
1. The category of 5 modules 261
2. Categories of i? modules 263
3. The algebraic theory of i? modules 265
4. The homotopical theory of i? ring spectra 267
5. Categories of il algebra 271
6. Bousfield localizations of iJ modules and algebras 274
7. Topological Hochschild homology and cohomology 277
8. The construction of THH via the standard complex 279
Chapter XXIV. Brave new equivariant foundations (by A. D.
Elmendorf, L. G. Lewis, Jr., and J. P. May) 283
1. The category of L spectra 283
2. Aao and Eoo ring spectra and S algebras 286
3. Alternative perspectives on equivariance 288
4. The construction of equivariant algebras and modules 291
5. Comparisons of categories of L G spectra 295
Chapter XXV. Brave new equivariant algebra (by J. P. C.
Greenlees and J. P. May) 299
1. Introduction 299
2. Local and Cech cohomology in algebra 300
3. Brave new versions of local and Cech cohomology 301
4. Localization theorems in equivariant homology 302
5. Completions, completion theorems, and local homology 305
6. A proof and generalization of the localization theorem 307
7. The application to if theory 310
8. Local Tate cohomology 311
Chapter XXVI. Localization and completion in complex bordism
(by J. P. C. Greenlees and J. P. May) 315
1. The localization theorem for stable complex bordism 315
2. An outline of the proof 316
3. The norm map and its properties 318
4. The idea behind the construciton of norm maps 320
5. Global ^ functors with smash product 322
6. The definition of the norm map 325
7. The splitting of MUG as an algebra 326
Chapter XXVII. A completion theorem in complex cobordism
(by G. Comezafia and J. P. May) 327
1. Statement of the theorem and preliminary results 327
CONTENTS xiii
2. Gysin sequences 329
3. Iterated completions 330
Chapter XXVIII, Calculations in complex equivariant bordism
(by G. Comezana) 333
1. Notations and terminology 333
2. Stably almost complex structures and bordism 334
3. Tangential structures 336
4. Calculational tools 339
5. Statements of the main results 342
6. Preliminary lemmas and families in G x S1 343
7. On the families 9 in G x S1 344
8. Passing from G to G x S1 and GxZk 349
Bibliography 353
Index 361
|
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| spelling | Equivariant homotopy and cohomology theory dedicated to the memory of Robert J. Piacenza J. P. May ... Providence, RI American Mathematical Society 1996 XIII, 366 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Regional Conference Series in Mathematics 91 Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Homologietheorie (DE-588)4141714-8 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content (DE-588)4016928-5 Festschrift gnd-content (DE-588)1071861417 Konferenzschrift gnd-content Homotopietheorie (DE-588)4128142-1 s DE-604 Homologietheorie (DE-588)4141714-8 s May, Jon Peter 1939- Sonstige (DE-588)122391810 oth Piacenza, Robert John 1943-1995 (DE-588)1012154157 hnr Regional Conference Series in Mathematics 91 (DE-604)BV000004346 91 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007551276&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Equivariant homotopy and cohomology theory dedicated to the memory of Robert J. Piacenza Regional Conference Series in Mathematics Homotopietheorie (DE-588)4128142-1 gnd Homologietheorie (DE-588)4141714-8 gnd |
| subject_GND | (DE-588)4128142-1 (DE-588)4141714-8 (DE-588)4143413-4 (DE-588)4016928-5 (DE-588)1071861417 |
| title | Equivariant homotopy and cohomology theory dedicated to the memory of Robert J. Piacenza |
| title_auth | Equivariant homotopy and cohomology theory dedicated to the memory of Robert J. Piacenza |
| title_exact_search | Equivariant homotopy and cohomology theory dedicated to the memory of Robert J. Piacenza |
| title_full | Equivariant homotopy and cohomology theory dedicated to the memory of Robert J. Piacenza J. P. May ... |
| title_fullStr | Equivariant homotopy and cohomology theory dedicated to the memory of Robert J. Piacenza J. P. May ... |
| title_full_unstemmed | Equivariant homotopy and cohomology theory dedicated to the memory of Robert J. Piacenza J. P. May ... |
| title_short | Equivariant homotopy and cohomology theory |
| title_sort | equivariant homotopy and cohomology theory dedicated to the memory of robert j piacenza |
| title_sub | dedicated to the memory of Robert J. Piacenza |
| topic | Homotopietheorie (DE-588)4128142-1 gnd Homologietheorie (DE-588)4141714-8 gnd |
| topic_facet | Homotopietheorie Homologietheorie Aufsatzsammlung Festschrift Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007551276&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004346 |
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