Groups with the Haagerup property: Gromov's a-T-menability
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Basel ; Boston ; Berlin
Birkhäuser
2001
|
| Schriftenreihe: | Progress in mathematics
197 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 115 - 123 |
| Beschreibung: | VII, 126 S. graph. Darst. : 24 cm |
| ISBN: | 3764365986 |
Internformat
MARC
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| 245 | 1 | 0 | |a Groups with the Haagerup property |b Gromov's a-T-menability |c Pierre-Alain Cherix ... |
| 264 | 1 | |a Basel ; Boston ; Berlin |b Birkhäuser |c 2001 | |
| 300 | |a VII, 126 S. |b graph. Darst. : 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 197 | |
| 500 | |a Literaturverz. S. 115 - 123 | ||
| 650 | 7 | |a Lokaal compacte groepen |2 gtt | |
| 650 | 7 | |a Presentatie |2 gtt | |
| 650 | 7 | |a TEORIA DOS GRUPOS (COLETÂNEA) |2 larpcal | |
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Datensatz im Suchindex
| _version_ | 1804128663902355456 |
|---|---|
| adam_text | Contents
1 Introduction
by Alain Valette
1.1 Basic definitions 1
1.1.1 The Haagerup property, or a T menability 1
1.1.2 Kazhdan s property (T) 2
1.2 Examples 2
1.2.1 Compact groups 3
1.2.2 SO(n, 1) and SU(n, 1) 3
1.2.3 Groups acting properly on trees 3
1.2.4 Groups acting properly on R trees 4
1.2.5 Coxeter groups 4
1.2.6 Amenable groups 4
1.2.7 Groups acting on spaces with walls 4
1.3 What is the Haagerup property good for? 5
1.3.1 Harmonic analysis: weak amenability 6
1.3.2 K amenability 7
1.3.3 The Baum Connes conjecture 8
1.4 What this book is about 10
2 Dynamical Characterizations
by Paul Jolissaint
2.1 Definitions and statements of results 15
2.2 Actions on measure spaces 21
2.3 Actions on factors 25
3 Simple Lie Groups of Rank One
by Pierre Julg
3.1 The Busemann cocycle and the
Gromov scalar product 34
3.2 Construction of a quadratic form 35
3.3 Positivity 37
3.4 The link with complementary series 38
vi Contents
4 Classification of Lie Groups with
the Haagerup Property
by Pierre Alain Cherix, Michael Cowling
and Alain Valette
4.0 Introduction 41
4.1 Step one 42
4.1.1 The fine structure of Lie groups 42
4.1.2 A criterion for relative property (T) 44
4.1.3 Conclusion of step one 46
4.2 Step two 46
4.2.1 The generalized Haagerup property 46
4.2.2 Amenable groups 54
4.2.3 Simple Lie groups 56
4.2.4 A covering group 56
4.2.5 Spherical functions 57
4.2.6 The group SU(n, 1) 59
4.2.7 The groups SO(n, 1) and SU(n, 1) 60
4.2.8 Conclusion of step two 60
5 The Radial Haagerup Property
by Michael Cowling
5.0 Introduction 63
5.1 The geometry of harmonic NA groups 64
5.2 Harmonic analysis on H type groups 66
5.3 Analysis on harmonic NA groups 72
5.4 Positive definite spherical functions 75
5.5 Appendix on special functions 82
6 Discrete Groups
by Paul Jolissaint, Pierre Julg
and Alain Valette
6.1 Some hereditary results 85
6.2 Groups acting on trees 91
6.3 Group presentations 97
6.4 Appendix: Completely positive maps
on amalgamated products,
by Paul Jolissaint 99
7 Open Questions and Partial Results
by Alain Valette
7.1 Obstructions to the Haagerup property 105
7.2 Classes of groups 105
7.2.1 One relator groups 105
Contents vii
7.2.2 Three manifold groups 106
7.2.3 Braid groups 107
7.3 Group constructions 107
7.3.1 Semi direct products 107
7.3.2 Actions on trees 107
7.3.3 Central extensions 108
7.4 Geometric characterizations 109
7.4.1 Chasles relation 109
7.4.2 Some cute and sexy spaces 111
7.5 Other dynamical characterizations 112
7.5.1 Actions on infinite measure spaces 112
7.5.2 Invariant probability measures 113
Bibliography 115
Index 125
|
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| id | DE-604.BV013832438 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:52:50Z |
| institution | BVB |
| isbn | 3764365986 |
| language | English |
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| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Groups with the Haagerup property Gromov's a-T-menability Pierre-Alain Cherix ... Basel ; Boston ; Berlin Birkhäuser 2001 VII, 126 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 197 Literaturverz. S. 115 - 123 Lokaal compacte groepen gtt Presentatie gtt TEORIA DOS GRUPOS (COLETÂNEA) larpcal Group theory Gruppentheorie (DE-588)4072157-7 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Gruppentheorie (DE-588)4072157-7 s DE-604 Cherix, Pierre-Alain 1966- Sonstige (DE-588)122947525 oth Progress in mathematics 197 (DE-604)BV000004120 197 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009460838&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Groups with the Haagerup property Gromov's a-T-menability Progress in mathematics Lokaal compacte groepen gtt Presentatie gtt TEORIA DOS GRUPOS (COLETÂNEA) larpcal Group theory Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4143413-4 |
| title | Groups with the Haagerup property Gromov's a-T-menability |
| title_auth | Groups with the Haagerup property Gromov's a-T-menability |
| title_exact_search | Groups with the Haagerup property Gromov's a-T-menability |
| title_full | Groups with the Haagerup property Gromov's a-T-menability Pierre-Alain Cherix ... |
| title_fullStr | Groups with the Haagerup property Gromov's a-T-menability Pierre-Alain Cherix ... |
| title_full_unstemmed | Groups with the Haagerup property Gromov's a-T-menability Pierre-Alain Cherix ... |
| title_short | Groups with the Haagerup property |
| title_sort | groups with the haagerup property gromov s a t menability |
| title_sub | Gromov's a-T-menability |
| topic | Lokaal compacte groepen gtt Presentatie gtt TEORIA DOS GRUPOS (COLETÂNEA) larpcal Group theory Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Lokaal compacte groepen Presentatie TEORIA DOS GRUPOS (COLETÂNEA) Group theory Gruppentheorie Aufsatzsammlung |
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