Homology of classical groups over finite fields and their associated infinite loop spaces:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1978
|
| Schriftenreihe: | Lecture notes in mathematics
674 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 434 S. |
| ISBN: | 3540089322 0387089322 |
Internformat
MARC
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| 100 | 1 | |a Fiedorowicz, Zbigniew |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Homology of classical groups over finite fields and their associated infinite loop spaces |c Zbigniew Fiedorowicz ; Stewart Priddy |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1978 | |
| 300 | |a VI, 434 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 674 | |
| 650 | 4 | |a Corps algébriques | |
| 650 | 4 | |a Espaces de lacets | |
| 650 | 4 | |a Groupes linéaires algébriques | |
| 650 | 4 | |a Homologie | |
| 650 | 7 | |a Homologie |2 gtt | |
| 650 | 4 | |a Finite fields (Algebra) | |
| 650 | 4 | |a Homology theory | |
| 650 | 4 | |a Infinite loop spaces | |
| 650 | 4 | |a Linear algebraic groups | |
| 650 | 0 | 7 | |a Gruppentheorie |0 (DE-588)4072157-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Galois-Feld |0 (DE-588)4155896-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Klassische Gruppe |0 (DE-588)4164040-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Homologie |0 (DE-588)4141951-0 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Priddy, Stewart |e Verfasser |4 aut | |
| 830 | 0 | |a Lecture notes in mathematics |v 674 |w (DE-604)BV000676446 |9 674 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-001480577 | ||
Datensatz im Suchindex
| _version_ | 1804116709507858432 |
|---|---|
| adam_text | Table of Contents
Introduction 1
Chapter I Infinite Loop Spaces Associated with ImJ 9
1. Introduction 9
2. The real image of J Spaces 10
3. The mod 2 homology of JO(q) 17
4. The symplectic and complex image of J Spaces „ 20
5. The odd primary homology of JO(q) 24
6. The odd primary homology of JSp(q) and JU(+q) 30
7. The integral cohomology of JO(q) 32
8. The integral cohomology of JSp(q) and JU(+q) 45
Chapter II Permutative Categories of classical Groups over
Finite Fields 49
1. Introduction 49
2. Permutative categories and their associated infinite
loop Spaces 49
3. The orthogonal groups and their subgroups 67
4. Quadratic forms and extraordinary orthogonal groups.... 82
5. Spinor groups over finite fields 97
6. The general linear, symplectic and unitary groups 110
7. Orthogonal groups over finite fields of
characteristic 2 117
8. Permutative functors associated with the classical
groups 145
IV
Chapter III K Theory of Finite Fields and the ImJ Spaces.... 166
1. Introductton 166
2. The Brauer lift 166
3. The main results 176
4. Mod p behavior of the classical groups 186
5. General pattern of arguments at noncharacteristic
primes: determining homology generators and relations
for the classical groups 197
6. General pattern of arguments at noncharacteristic
primes: the Brauer lift 212
7. Algebraic closures of finite fields 224
Chapter IV Calculations at the prime 2 250
1. Introduction 250.
2. H*B(5(E ) and H*r0B©(E ) 250
3. The automorphism § 263
4. The cohomology rings H*B0(n,E ) and H*B0(n,E ) 266
5. H*Bjf(Iq) arid H*r0B,4p(! ) 277
6. The cohomology rings H*BSp(2m,E ) 282
7 H*B/T£(t ) and H*r0B.#£ (E ); H*BW(I 2) and
q q q
H^r0BW(E ) 283
q
8. The cohomology rings H*BGL(n,E ) and H*BU(n,E 2) 287
q q
Chapter V Calculations at Odd Primes 293
1. Introduction 293
2. H.Bff(I ) and H*rnB0(E ) 293
3. H*Bjp(Eq) and H^rQB^(Eq) 301
4. H*B0 0;C(E ), q even 3O3
V
5. H^B^dfd ) and H*r0B^jf (I ) ; H*B#(I 2) and
q q q
H^rQBti(E 2) 305
q
6. The cohomology rings H*B0(n,E ), H*B0(n,E ),
H*BSp(2n,E ), H*BGL(n,I ), H*BU(n,E 2) 31°
q q q
Chapter VI The Homology of Certain Finite Groups 313
1. Introduction 313
2. Cyclic groups 313
3. Dihedral groups.D 322
4. 0(2,Iq) 324
5. SL(2,E ) and Sp(4,E ) 329
6. GL(2,Eq) and U(2,Eq) 337
Chapter VII Detection Theorems at the Prime 2 343
1. Introduction 343
2. 0(n,r ) and 0(n,Eq) 343
3. Sp(2n,E ) 3S1
4. GL(n,E ) and U(n,E 2) 352
q q
Chapter VIII Detection Theorems at Odd Primes 355
1. Introduction 355
2. Number theoretic preliminaries 355
3. GL(m,E ) q = 1 (mod l) and U(m,I 2) q = 1 (mod t) 359
q q
4. 0(m,E ) and 0(m,E ) 36S
5. Sp(2m,Eq) 376
6. GL(m,F ) 379
7. U(m,E 2) 381
q
VI
Chapter IX Homology Operations Associated with the
Classical Groups 386
1. Introduction 386
2. Homology operations in H^Btf(I ) and H^rB0(i: ) 389
3. Homology operations in H^B^(E ) and H^rB^(I ) 397
4. Homology operations in H_,.B .#/(I ) and H^rB^jf (I )
H*B?/(E 2), and H^rB!Z(E ) 401
Appendix Multiplicative Homology Operations Associated
with the Orthogonal Groups 407
1. Introduction 407
2. Bipermutative categories and their associated infinite
loop Spaces 402
3. The multiplicative structure of U.B (E ) and
¦k q
njTBÖd ) 413
* q
Bibliography 429
Index 433
|
| any_adam_object | 1 |
| author | Fiedorowicz, Zbigniew Priddy, Stewart |
| author_facet | Fiedorowicz, Zbigniew Priddy, Stewart |
| author_role | aut aut |
| author_sort | Fiedorowicz, Zbigniew |
| author_variant | z f zf s p sp |
| building | Verbundindex |
| bvnumber | BV002253156 |
| callnumber-first | Q - Science |
| callnumber-label | QA3 |
| callnumber-raw | QA3 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)4211176 (DE-599)BVBBV002253156 |
| dewey-full | 510/.8 512/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 512 - Algebra |
| dewey-raw | 510/.8 512/.2 |
| dewey-search | 510/.8 512/.2 |
| dewey-sort | 3510 18 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002253156 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:49Z |
| institution | BVB |
| isbn | 3540089322 0387089322 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001480577 |
| oclc_num | 4211176 |
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| physical | VI, 434 S. |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Fiedorowicz, Zbigniew Verfasser aut Homology of classical groups over finite fields and their associated infinite loop spaces Zbigniew Fiedorowicz ; Stewart Priddy Berlin [u.a.] Springer 1978 VI, 434 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 674 Corps algébriques Espaces de lacets Groupes linéaires algébriques Homologie Homologie gtt Finite fields (Algebra) Homology theory Infinite loop spaces Linear algebraic groups Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Galois-Feld (DE-588)4155896-0 gnd rswk-swf Klassische Gruppe (DE-588)4164040-8 gnd rswk-swf Homologie (DE-588)4141951-0 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s Homologie (DE-588)4141951-0 s Galois-Feld (DE-588)4155896-0 s DE-604 Klassische Gruppe (DE-588)4164040-8 s Priddy, Stewart Verfasser aut Lecture notes in mathematics 674 (DE-604)BV000676446 674 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001480577&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fiedorowicz, Zbigniew Priddy, Stewart Homology of classical groups over finite fields and their associated infinite loop spaces Lecture notes in mathematics Corps algébriques Espaces de lacets Groupes linéaires algébriques Homologie Homologie gtt Finite fields (Algebra) Homology theory Infinite loop spaces Linear algebraic groups Gruppentheorie (DE-588)4072157-7 gnd Galois-Feld (DE-588)4155896-0 gnd Klassische Gruppe (DE-588)4164040-8 gnd Homologie (DE-588)4141951-0 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4155896-0 (DE-588)4164040-8 (DE-588)4141951-0 |
| title | Homology of classical groups over finite fields and their associated infinite loop spaces |
| title_auth | Homology of classical groups over finite fields and their associated infinite loop spaces |
| title_exact_search | Homology of classical groups over finite fields and their associated infinite loop spaces |
| title_full | Homology of classical groups over finite fields and their associated infinite loop spaces Zbigniew Fiedorowicz ; Stewart Priddy |
| title_fullStr | Homology of classical groups over finite fields and their associated infinite loop spaces Zbigniew Fiedorowicz ; Stewart Priddy |
| title_full_unstemmed | Homology of classical groups over finite fields and their associated infinite loop spaces Zbigniew Fiedorowicz ; Stewart Priddy |
| title_short | Homology of classical groups over finite fields and their associated infinite loop spaces |
| title_sort | homology of classical groups over finite fields and their associated infinite loop spaces |
| topic | Corps algébriques Espaces de lacets Groupes linéaires algébriques Homologie Homologie gtt Finite fields (Algebra) Homology theory Infinite loop spaces Linear algebraic groups Gruppentheorie (DE-588)4072157-7 gnd Galois-Feld (DE-588)4155896-0 gnd Klassische Gruppe (DE-588)4164040-8 gnd Homologie (DE-588)4141951-0 gnd |
| topic_facet | Corps algébriques Espaces de lacets Groupes linéaires algébriques Homologie Finite fields (Algebra) Homology theory Infinite loop spaces Linear algebraic groups Gruppentheorie Galois-Feld Klassische Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001480577&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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