Continuous bounded cohomology of locally compact groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London
Springer
2001
|
| Series: | Lecture notes in mathematics
1758 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 214 S. graph. Darst. |
| ISBN: | 3540420541 |
Staff View
MARC
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| 245 | 1 | 0 | |a Continuous bounded cohomology of locally compact groups |c Nicolas Monod |
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Record in the Search Index
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| adam_text | Contents
Preface v
Introduction 1
Chapter I. Banach modules, L°° spaces 9
1. Banach modules 9
1.1. Notations and first definitions 9
1.2. Elementary constructions 13
1.3. Spaces of continuous functions 17
2. L°° spaces 17
2.1. Regular spaces 18
2.2. Measurable maps 19
2.3. Duality 20
2.4. Double structure on L^.(G,E) 21
2.5. £°° spaces 23
3. Integration 24
3.1. Bochner s integral 24
3.2. Gelfand Dunford integral 26
3.3. More on continuity 29
Chapter II. Relative injectivity and amenable actions 31
4. Relative injectivity 31
4.1. Definitions 32
4.2. Comments on admissible G morphisms 33
4.3. First properties 35
4.4. Fundamental examples 37
4.5. Proper G spaces 39
5. Amenability and amenable actions 45
5.1. Prelude on relative injectivity 45
5.2. Relative injectivity for subgroups, 1 47
5.3. Amenable actions : definitions 48
5.4. Basic examples 52
5.5. Admissibility of the coefficient inclusion 54
5.6. A result on equivariant means 55
5.7. A characterization of amenable actions 58
5.8. Relative injectivity for subgroups, II 59
viii CONTENTS
Chapter III. Definition and characterization of
continuous bounded cohomology 61
6. A naive definition 61
6.1. The canonical complex 61
6.2. Low degree, I 64
7. The functorial characterization 66
7.1. Basic definitions 67
7.2. Statement of the functorial characterization 70
7.3. The canonical semi norm 74
7.4. Examples of resolutions of Banach modules 76
7.5. Examples of resolutions of coefficient modules 82
8. Functoriality 91
8.1. Covariance 91
8.2. The long exact sequence 92
8.3. The coefficient representation 100
8.4. Contravariance 101
8.5. Inflation 103
8.6. Restriction 105
8.7. The conjugation action on cohomology 110
8.8. A closer look at the action on cohomology 114
9. Continuous cohomology and the comparison map 119
9.1. Continuous cohomology 120
9.2. The comparison map 122
9.3. Examples and remarks 124
Chapter IV. Cohomological techniques 129
10. General techniques 129
10.1. Induction 129
10.2. Lp induction 136
10.3. Dimension shifting 141
11. Double ergodicity 143
11.1. Definition and elementary properties 143
11.2. Classical examples 147
11.3. The group G* 148
11.4. Low degree, II 152
12. Hochschild Serre spectral sequence 155
12.1. General setup 157
12.2. The first tableaux 160
12.3. Exact sequences 163
12.4. Exact sequences for discrete groups 166
Chapter V. Towards applications 169
13. Interpretations of EH*b 170
13.1. Rough actions 170
13.2. Property (TT) 172
13.3. Quasi morphisms 175
CONTENTS ix
13.4. Algebraic groups and their lattices 178
13.5. Actions on the circle 182
13.6. Mapping class group and PSU(n, 1) 184
14. General irreducible lattices 185
U.I. Irreducibility 185
14.2. The general results and applications 188
14.3. Classical irreducible lattices 192
14.4. Lattices in products of trees 196
14.5 The adelic case 197
Bibliography 203
Index 211
|
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| id | DE-604.BV013717414 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:50:44Z |
| institution | BVB |
| isbn | 3540420541 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009373818 |
| oclc_num | 46937548 |
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| physical | IX, 214 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Monod, Nicolas 1973- Verfasser (DE-588)122848896 aut Continuous bounded cohomology of locally compact groups Nicolas Monod Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London Springer 2001 IX, 214 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1758 Cohomologie gtt Groupes localement compacts Homologie Topologische groepen gtt Homology theory Locally compact groups Lokal kompakte Gruppe (DE-588)4168094-7 gnd rswk-swf Stetige Kohomologie (DE-588)4183163-9 gnd rswk-swf Lokal kompakte Gruppe (DE-588)4168094-7 s Stetige Kohomologie (DE-588)4183163-9 s DE-604 Lecture notes in mathematics 1758 (DE-604)BV000676446 1758 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009373818&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Monod, Nicolas 1973- Continuous bounded cohomology of locally compact groups Lecture notes in mathematics Cohomologie gtt Groupes localement compacts Homologie Topologische groepen gtt Homology theory Locally compact groups Lokal kompakte Gruppe (DE-588)4168094-7 gnd Stetige Kohomologie (DE-588)4183163-9 gnd |
| subject_GND | (DE-588)4168094-7 (DE-588)4183163-9 |
| title | Continuous bounded cohomology of locally compact groups |
| title_auth | Continuous bounded cohomology of locally compact groups |
| title_exact_search | Continuous bounded cohomology of locally compact groups |
| title_full | Continuous bounded cohomology of locally compact groups Nicolas Monod |
| title_fullStr | Continuous bounded cohomology of locally compact groups Nicolas Monod |
| title_full_unstemmed | Continuous bounded cohomology of locally compact groups Nicolas Monod |
| title_short | Continuous bounded cohomology of locally compact groups |
| title_sort | continuous bounded cohomology of locally compact groups |
| topic | Cohomologie gtt Groupes localement compacts Homologie Topologische groepen gtt Homology theory Locally compact groups Lokal kompakte Gruppe (DE-588)4168094-7 gnd Stetige Kohomologie (DE-588)4183163-9 gnd |
| topic_facet | Cohomologie Groupes localement compacts Homologie Topologische groepen Homology theory Locally compact groups Lokal kompakte Gruppe Stetige Kohomologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009373818&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT monodnicolas continuousboundedcohomologyoflocallycompactgroups |