The regulators of Beilinson and Borel:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2002
|
| Schriftenreihe: | CRM Monograph series
15 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009739435&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 104 S. |
| ISBN: | 0821826301 |
Internformat
MARC
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| 245 | 1 | 0 | |a The regulators of Beilinson and Borel |c José I. Burgos Gil |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2002 | |
| 300 | |a XI, 104 S. | ||
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Datensatz im Suchindex
| _version_ | 1819370271498305536 |
|---|---|
| adam_text | Contents
Acknowledgments xi
Chapter 1. Introduction 1
Chapter 2. Simplicial and Cosimplicial Objects 5
2.1. Basic Definitions and Examples 5
2.2. Simplicial Abelian Groups 8
2.3. The Geometric Realization 10
2.4. Sheaves on Simplicial Topological Spaces 11
2.5. Principal Bundles on Simplicial Manifolds 12
2.6. The de Rham Algebra of a Simplicial Manifold 13
Chapter 3. // Spaces and Hopf Algebras 15
3.1. Definitions 15
3.2. Some Examples 18
3.3. The Structure of Hopf Algebras 19
3.4. Rational Homotopy of // Spaces 20
Chapter 4. The Cohomology of the General Linear Group 23
4.1. The General Linear Group and the Stiefel Manifolds 23
4.2. Classifying Spaces and Characteristic Classes 25
4.3. The Suspension 27
4.4. The Stability of Homology and Cohomology 29
4.5. The Stable Homotopy of the General Linear Group 31
4.6. Other Consequences of Bott s Periodicity Theorem 32
Chapter 5. Lie Algebra Cohomology and the Weil Algebra 35
5.1. de Rham Cohomology of a Lie Group 35
5.2. Reductive Lie Algebras 38
5.3. Characteristic Classes in de Rham Cohomology 40
5.4. The Suspension in the Weil Algebra 45
5.5. Relative Lie Algebra Cohomology 48
Chapter 6. Group Cohomology and the van Est Isomorphism 51
6.1. Group Homology and Cohomology 51
6.2. Continuous Group Cohomology 53
6.3. Computation of Continuous Cohomology 54
ix
x CONTENTS
Chapter 7. Small Cosimplicial Algebras 57
7.1. Cosimplicial Algebras 57
7.2. Small Algebras 60
Chapter 8. Higher Diagonals and Differential Forms 65
8.1. The Sheaf of Differential Forms 65
8.2. The Weil Algebra Revisited 70
8.3. A Description of the van Est Isomorphism 72
Chapter 9. Borel s Regulator 75
9.1. Algebraic ^ Theory of Rings 75
9.2. Definition of Borel s Regulator 76
9.3. The Rank of the Groups Km(x)) 78
9.4. The Values of the Zeta Functions 79
9.5. A Renormalization of Borel s Regulator 80
9.6. Borel Elements 86
9.7. Explicit Representatives of the Borel Element 87
Chapter 10. Beilinson s Regulator 89
10.1. Deligne Beilinson Cohomology 89
10.2. Deligne Beilinson Cohomology of B.GLn(C) 92
10.3. The Definition of Beilinson s Regulator 93
10.4. The Comparison Between the Regulators 95
Bibliography 99
Index 103
|
| any_adam_object | 1 |
| author | Burgos Gil, José I. 1962- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.74 |
| dewey-search | 512/.74 |
| dewey-sort | 3512 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV014206897 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T11:01:14Z |
| institution | BVB |
| isbn | 0821826301 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009739435 |
| oclc_num | 48100389 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-824 DE-11 DE-384 |
| owner_facet | DE-355 DE-BY-UBR DE-824 DE-11 DE-384 |
| physical | XI, 104 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | CRM Monograph series |
| series2 | CRM Monograph series |
| spellingShingle | Burgos Gil, José I. 1962- The regulators of Beilinson and Borel CRM Monograph series Regulators (Mathematics) Regulator Mathematik (DE-588)4385847-8 gnd |
| subject_GND | (DE-588)4385847-8 |
| title | The regulators of Beilinson and Borel |
| title_auth | The regulators of Beilinson and Borel |
| title_exact_search | The regulators of Beilinson and Borel |
| title_full | The regulators of Beilinson and Borel José I. Burgos Gil |
| title_fullStr | The regulators of Beilinson and Borel José I. Burgos Gil |
| title_full_unstemmed | The regulators of Beilinson and Borel José I. Burgos Gil |
| title_short | The regulators of Beilinson and Borel |
| title_sort | the regulators of beilinson and borel |
| topic | Regulators (Mathematics) Regulator Mathematik (DE-588)4385847-8 gnd |
| topic_facet | Regulators (Mathematics) Regulator Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009739435&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007928388 |
| work_keys_str_mv | AT burgosgiljosei theregulatorsofbeilinsonandborel |