Rational S 1 -equivariant stable homotopy theory:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
1999
|
| Series: | American Mathematical Society: Memoirs of the American Mathematical Society
661 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008495813&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | "Volume 138, number 661 (end of volume)." |
| Physical Description: | XII, 289 S. |
| ISBN: | 0821810014 |
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| 245 | 1 | 0 | |a Rational S 1 -equivariant stable homotopy theory |c J. P. C. Greenlees |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1999 | |
| 300 | |a XII, 289 S. | ||
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| 490 | 1 | |a American Mathematical Society: Memoirs of the American Mathematical Society |v 661 | |
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Record in the Search Index
| DE-BY-TUM_call_number | 0102 MAT 001z 2001 B 990-658/661 |
|---|---|
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| adam_text | Contents
Chapter 0. General Introduction. 1
0.1. Motivation. 1
0.2. Overview. 1
Part I. The algebraic model of rational T spectra. 13
Chapter 1. Introduction to Part I. 15
1.1. Outline of the algebraic models. 15
1.2. Reading Guide for Part I. 19
1.3. Haeberly s example. 20
1.4. McClure s Chern character isomorphism for ^ spaces. 21
Chapter 2. Topological building blocks. 25
2.1. Natural cells and basic cells. 25
2.2. Separating isotropy types. 29
2.3. The single strand spectra E{H). 33
2.4. Operations: self maps of E{H). 36
Chapter 3. Maps between .F free T spectra. 39
3.1. The Adams short exact sequence. 39
3.2. The Whitehead and Hurewicz theorems for T spectra over H. 39
3.3. The injective case. 40
3.4. Injectives in the category of torsion Q[cH] modules. 41
3.5. Proof of Theorem 3.1.1. 42
Chapter 4. Categorical reprocessing. 45
4.1. Recollections about derived categories. 45
4.2. Split linear triangulated categories. 49
4.3. The uniqueness theorem. 51
4.4. The algebraicization of the category of T spectra over H. 54
4.5. The algebraicization of the category of ^ spectra. 55
4.6. Euler classes revisited. 57
Chapter 5. Assembly and the standard model. 59
5.1. Assembly. 59
5.2. The ring tf. 61
5.3. Global assembly. 63
vii
viii CONTENTS
5.4. The standard model category. 64
5.5. Homological algebra in the standard model. 65
5.6. The algebraicization of rational T spectra. 67
5.7. Maps between injective spectra. 71
5.8. Algebraic cells and spheres. 73
5.9. Explicit models. 75
5.10. Hausdorff modules. 77
Chapter 6. The torsion model. 79
6.1. Practical calculations. 79
6.2. The torsion model. 81
6.3. Homological algebra in the torsion model. 82
6.4. The derived category of the torsion model. 83
6.5. Equivalence of derived categories of standard and torsion models. 85
6.6. Relationship to topology. 87
Part II. Change of groups functors in algebra and topology. 89
Chapter 7. Introduction to Part II. 91
7.1. General outline. 91
7.2. Modelling functors changing equivariance. 93
7.3. Functors between split triangulated categories. 95
Chapter 8. Induction, coinduction and geometric fixed points. 99
8.1. Forgetful, induction and coinduction functors. 99
8.2. The Lewis May T fixed point functor. 101
8.3. An algebraic model for geometric fixed points. 103
8.4. Analysis of geometric fixed points. 105
Chapter 9. Algebraic inflation and deflation. 109
9.1. Algebraic inflation and deflation of Ojr modules. 109
9.2. Inflation and its right adjoint on the torsion model category. Ill
Chapter 10. Inflation, Lewis May fixed points and quotients. 115
10.1. The topological inflation and Lewis May fixed point functors. 115
10.2. Inflation on objects. 117
10.3. Correspondence of Algebraic and geometric inflation functors. 119
10.4. A direct approach to the Lewis May fixed point functor. 121
10.5. The homotopy type of Lewis May fixed points. 123
10.6. Quotient functors. 126
Part III. Applications. 127
Chapter 11. Introduction to Part III. 129
11.1. General Outline. 129
11.2. Prospects and problems. 131
CONTENTS ix
Chapter 12. Homotopy Mackey functors and related constructions. 133
12.1. The homotopy Mackey functor on A 134
12.2. Eilenberg MacLane spectra. 137
12.3. coMackey functors and spectra representing ordinary homology. 140
12.4. Brown Comenetz spectra. 142
Chapter 13. Classical miscellany. 147
13.1. The collapse of the Atiyah Hirzebruch spectral sequence. 147
13.2. Orbit category resolutions. 150
13.3. Suspension spectra. 151
13.4. K theory revisited. 152
13.5. The geometric equivariant rational Segal conjecture for T. 156
Chapter 14. Cyclic and Tate cohomology. 159
14.1. Cyclic cohomology. 159
14.2. Rational Tate spectra. 160
14.3. The integral T equivariant Tate spectrum for complex K theory. 161
Chapter 15. Cyclotomic spectra and topological cyclic cohomology. 165
15.1. Cyclotomic spectra. 165
15.2. Free loop spaces and THH. 169
15.3. The definition of topological cyclic homology. 170
15.4. Topological cyclic homology of rational spectra. 172
Part IV. Tensor and Horn in algebra and topology. 177
Chapter 16. Introduction. 179
16.1. General outline. 179
16.2. Modelling of the smash product and the function spectrum. 180
16.3. Torsion Functors. 182
16.4. Modelling of the product spectrum. 183
16.5. Modelling the Lewis May fixed point functor. 183
16.6. Genera of small objects. 184
Chapter 17. Torsion functors. 185
17.1. Context. 185
17.2. Torsion fc[c] modules. 187
17.3. ^ finite torsion O^ modules. 188
17.4. The torsion model. 190
Chapter 18. Torsion functors for the semifree standard model. 193
18.1. Maps out of spheres. 193
18.2. The torsion functor. 194
18.3. Calculations of the torsion functor. 197
Chapter 19. Wide spheres and representing the semifree torsion functor. 201
19.1. Some indecomposable objects. 201
x CONTENTS
19.2. Wide spheres. 205
19.3. Corepresenting the torsion functor. 207
19.4. Duals of wide spheres. 210
19.5. Representing the torsion functor. 212
Chapter 20. Torsion functors for the full standard model. 215
20.1. Maps out of spheres. 215
20.2. The torsion functor. 216
20.3. Calculations of the torsion functor. 217
Chapter 21. Product functors. 219
21.1. General discussion. 219
21.2. Torsion modules. 220
21.3. The torsion model. 221
21.4. The standard models. 222
Chapter 22. The tensor Horn adjunction. 225
22.1. General discussion. 225
22.2. Calculations in the semifree standard model. 226
22.3. Construction of the semifree Horn functor. 228
22.4. Flabbiness of the Horn object. 229
22.5. Calculations in the standard model. 230
22.6. Construction of the standard Horn functor. 231
Chapter 23. The derived tensor Horn adjunction. 233
23.1. The case of finite fiat dimension. 233
23.2. Flat dimension of the semifree category. 234
23.3. Flat dimension of the standard model. 234
23.4. The case without enough flat objects. 236
23.5. Torsion fc[c] modules. 238
Chapter 24. Smash products, function spectra and Lewis May fixed points. 241
24.1. Models of smash products. 241
24.2. Models of function spectra. 243
24.3. Proof of Theorem 24.2.1. 245
24.4. The Lewis May A fixed point functor. 248
Appendix A. Mackey functors. 253
Appendix B. Closed model categories. 259
Appendix C. Conventions. 265
C.I. Conventions for spaces and spectra. 265
C.2. Standing conventions. 267
Appendix D. Indices. 269
D.I. Index of definitions and terminology. 269
D.2. Index of notation. 274
CONTENTS xi
Appendix E. Summary of models. 285
E.I. The standard model. 285
E.2. The torsion model. 287
Bibliography 289
|
| any_adam_object | 1 |
| author | Greenlees, J. P. C. 1959- |
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| author_facet | Greenlees, J. P. C. 1959- |
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| dewey-ones | 510 - Mathematics |
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| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012515828 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:31:41Z |
| institution | BVB |
| isbn | 0821810014 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008495813 |
| oclc_num | 245674425 |
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| physical | XII, 289 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
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| publisher | American Math. Soc. |
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| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spellingShingle | Greenlees, J. P. C. 1959- Rational S 1 -equivariant stable homotopy theory American Mathematical Society: Memoirs of the American Mathematical Society Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4128142-1 |
| title | Rational S 1 -equivariant stable homotopy theory |
| title_auth | Rational S 1 -equivariant stable homotopy theory |
| title_exact_search | Rational S 1 -equivariant stable homotopy theory |
| title_full | Rational S 1 -equivariant stable homotopy theory J. P. C. Greenlees |
| title_fullStr | Rational S 1 -equivariant stable homotopy theory J. P. C. Greenlees |
| title_full_unstemmed | Rational S 1 -equivariant stable homotopy theory J. P. C. Greenlees |
| title_short | Rational S 1 -equivariant stable homotopy theory |
| title_sort | rational s 1 equivariant stable homotopy theory |
| topic | Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Homotopietheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008495813&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT greenleesjpc rationals1equivariantstablehomotopytheory |
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