Metric geometry of locally compact groups: winner of the 2016 EMS Monograph Award
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Zürich
European Mathematical Society Publishing House
[2016]
|
| Schriftenreihe: | EMS tracts in mathematics
25 |
| Schlagworte: | |
| Online-Zugang: | DE-188 DE-91 DE-19 DE-355 DE-703 Volltext Inhaltsverzeichnis |
| Beschreibung: | 1 Online-Ressource (viii, 235 Seiten) Diagramme |
| ISBN: | 9783037196663 |
| DOI: | 10.4171/166 |
Internformat
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| 653 | |a left-invariant metrics | ||
| 653 | |a Locally compact groups | ||
| 653 | |a coarse connectedness | ||
| 653 | |a compact generation | ||
| 653 | |a compact presentation | ||
| 653 | |a metric coarse equivalence | ||
| 653 | |a quasi-isometry | ||
| 653 | |a second countability | ||
| 653 | |a sigma-compactness | ||
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Datensatz im Suchindex
| _version_ | 1810452450306424832 |
|---|---|
| adam_text |
Titel: Metric geometry of locally compact groups
Autor: Cornulier, Yves
Jahr: 2016
Contents
1 Introduction. 1
1 .A Discrete groups as metric spaces. 1
1 .B Discrete groups and locally compact groups. 3
1 .C Three conditions on LC-groups. 4
1 .D Metric characterization. 6
1 .E On compact presentations. 8
l.F Outline of the book. 9
l.G Acknowledgements. 10
2 Basic properties. 11
2.A Topological spaces and pseudo-metric spaces . 12
2.B Metrizability and a -compactness. 19
2.C Compact generation . 26
2.D Miscellanea. 37
2.E Structure of LC-groups. 39
3 Metric coarse and large-scale categories. 53
3.A Coarsely Lipschitz and large-scale Lipschitz maps. 53
3.B Coarse properties and large-scale properties. 65
3.B.a Coarsely connected, coarsely geodesic,
and large-scale geodesic pseudo-metric spaces. 65
3.B.D Coarsely ultrametric pseudo-metric spaces. 70
3.B.C Asymptotic dimension. 72
3.C Metric lattices in pseudo-metric spaces. 73
3.D Growth and amenability. 77
3.D.a Growth for uniformly locally finite pseudo-metric spaces . 77
3.D.b Growth for uniformly coarsely proper pseudo-metric spaces
and a-compact LC-groups. 80
3.D.C Amenability. 88
3.E The coarse category. 92
4 Groups as pseudo-metric spaces. 95
4. A Adapted (pseudo-)metrics on o -compact groups. 95
4.B Pseudo-metrics on compactly generated groups. 99
4.C Actions of groups on pseudo-metric spaces. 107
4.D Local ellipticity. 114
4.E Capped subgroups. 121
4.F Amenable and geometrically amenable LC-groups. 127
viii Contents
5 Examples of compactly generated LC-groups.133
5.A Connected, abelian, nilpotent, Lie, and algebraic.133
5.B Isometry groups.139
5.C Lattices in LC-groups.146
6 Coarse simple connectedness.153
6.A Coarsely simply connected pseudo-metric spaces.153
6.B On simplicial complexes.157
6.C The Rips 2-complex of a pseudo-metric space.160
7 Bounded presentations .163
7. A Presentations with relators of bounded length .163
7.B The Rips complex of a bounded presentation.171
8 Compactly presented groups.173
8.A Definition and first examples.173
8.B Amalgamated products and HNN-extensions.184
8.C Homomorphisms to Z and splittings.192
8.C.a A topological version of the Bieri-Strebel splitting theorem . . 192
8.C.b Proofs.194
8.C.C Engulfing automorphisms.197
8.D Further examples .201
8.D.a Semidirect products with Z.201
8.D.b More general semidirect products, and SL"(K).204
Bibliography.213
Index.229 |
| any_adam_object | 1 |
| author | Cornulier, Yves 1981- La Harpe, Pierre de |
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| author_facet | Cornulier, Yves 1981- La Harpe, Pierre de |
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| dewey-ones | 510 - Mathematics |
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| dewey-search | 510 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.4171/166 |
| format | Electronic eBook |
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| spelling | Cornulier, Yves 1981- Verfasser (DE-588)1120024137 aut Metric geometry of locally compact groups winner of the 2016 EMS Monograph Award Yves Cornulier, Pierre de la Harpe Zürich European Mathematical Society Publishing House [2016] © 2016 1 Online-Ressource (viii, 235 Seiten) Diagramme txt rdacontent c rdamedia cr rdacarrier EMS tracts in mathematics 25 Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Lokal kompakte Gruppe (DE-588)4168094-7 gnd rswk-swf Graduate students and advanced undergraduate students mathematicians who wish some introduction to coarse geometry and locally compact groups. left-invariant metrics Locally compact groups coarse connectedness compact generation compact presentation metric coarse equivalence quasi-isometry second countability sigma-compactness Lokal kompakte Gruppe (DE-588)4168094-7 s Metrischer Raum (DE-588)4169745-5 s 1\p DE-604 La Harpe, Pierre de Verfasser (DE-588)108064158 aut European Mathematical Society Publishing House ETH-Zentrum SEW A27 (DE-588)1066118477 pbl Erscheint auch als Druck-Ausgabe 978-3-03719-166-8 EMS tracts in mathematics 25 (DE-604)BV043991716 25 https://doi.org/10.4171/166 Verlag URL des Erstveröffentlichers Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029261250&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cornulier, Yves 1981- La Harpe, Pierre de Metric geometry of locally compact groups winner of the 2016 EMS Monograph Award EMS tracts in mathematics Metrischer Raum (DE-588)4169745-5 gnd Lokal kompakte Gruppe (DE-588)4168094-7 gnd |
| subject_GND | (DE-588)4169745-5 (DE-588)4168094-7 |
| title | Metric geometry of locally compact groups winner of the 2016 EMS Monograph Award |
| title_auth | Metric geometry of locally compact groups winner of the 2016 EMS Monograph Award |
| title_exact_search | Metric geometry of locally compact groups winner of the 2016 EMS Monograph Award |
| title_full | Metric geometry of locally compact groups winner of the 2016 EMS Monograph Award Yves Cornulier, Pierre de la Harpe |
| title_fullStr | Metric geometry of locally compact groups winner of the 2016 EMS Monograph Award Yves Cornulier, Pierre de la Harpe |
| title_full_unstemmed | Metric geometry of locally compact groups winner of the 2016 EMS Monograph Award Yves Cornulier, Pierre de la Harpe |
| title_short | Metric geometry of locally compact groups |
| title_sort | metric geometry of locally compact groups winner of the 2016 ems monograph award |
| title_sub | winner of the 2016 EMS Monograph Award |
| topic | Metrischer Raum (DE-588)4169745-5 gnd Lokal kompakte Gruppe (DE-588)4168094-7 gnd |
| topic_facet | Metrischer Raum Lokal kompakte Gruppe |
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