Metric geometry of locally compact groups: winner of the 2016 EMS Monograph Award
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Zürich
European Mathematical Society Publishing House
[2016]
|
| Series: | EMS tracts in mathematics
25 |
| Subjects: | |
| Online Access: | DE-188 DE-91 DE-19 DE-355 DE-703 Volltext Inhaltsverzeichnis |
| Physical Description: | 1 Online-Ressource (viii, 235 Seiten) Diagramme |
| ISBN: | 9783037196663 |
| DOI: | 10.4171/166 |
Staff View
MARC
| LEADER | 00000nmm a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV043850933 | ||
| 003 | DE-604 | ||
| 005 | 20240917 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161028s2016 gw |||| o||u| ||||||eng d | ||
| 020 | |a 9783037196663 |c Online |9 978-3-03719-666-3 | ||
| 024 | 7 | |a 10.4171/166 |2 doi | |
| 035 | |a (OCoLC)964687686 | ||
| 035 | |a (DE-599)BVBBV043850933 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE | ||
| 049 | |a DE-19 |a DE-91 |a DE-188 |a DE-355 |a DE-703 |a DE-83 |a DE-11 | ||
| 082 | 0 | |a 510 |2 23 | |
| 084 | |a SK 260 |0 (DE-625)143227: |2 rvk | ||
| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Cornulier, Yves |d 1981- |e Verfasser |0 (DE-588)1120024137 |4 aut | |
| 245 | 1 | 0 | |a Metric geometry of locally compact groups |b winner of the 2016 EMS Monograph Award |c Yves Cornulier, Pierre de la Harpe |
| 264 | 1 | |a Zürich |b European Mathematical Society Publishing House |c [2016] | |
| 264 | 4 | |c © 2016 | |
| 300 | |a 1 Online-Ressource (viii, 235 Seiten) |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a EMS tracts in mathematics |v 25 | |
| 650 | 0 | 7 | |a Metrischer Raum |0 (DE-588)4169745-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lokal kompakte Gruppe |0 (DE-588)4168094-7 |2 gnd |9 rswk-swf |
| 653 | |a Graduate students and advanced undergraduate students mathematicians who wish some introduction to coarse geometry and locally compact groups. | ||
| 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 | ||
| 689 | 0 | 0 | |a Lokal kompakte Gruppe |0 (DE-588)4168094-7 |D s |
| 689 | 0 | 1 | |a Metrischer Raum |0 (DE-588)4169745-5 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a La Harpe, Pierre de |e Verfasser |0 (DE-588)108064158 |4 aut | |
| 710 | 2 | |a European Mathematical Society Publishing House ETH-Zentrum SEW A27 |0 (DE-588)1066118477 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-3-03719-166-8 |
| 830 | 0 | |a EMS tracts in mathematics |v 25 |w (DE-604)BV043991716 |9 25 | |
| 856 | 4 | 0 | |u https://doi.org/10.4171/166 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 912 | |a ZDB-147-EMB | ||
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-029261250 | |
| 966 | e | |u https://doi.org/10.4171/166 |l DE-188 |p ZDB-147-EMB |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.4171/166 |l DE-91 |p ZDB-147-EMB |q TUM_Serienkauf |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.4171/166 |l DE-19 |p ZDB-147-EMB |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.4171/166 |l DE-355 |p ZDB-147-EMB |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.4171/166 |l DE-703 |p ZDB-147-EMB |x Verlag |3 Volltext | |
Record in the Search Index
| _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 |
| author_GND | (DE-588)1120024137 (DE-588)108064158 |
| author_facet | Cornulier, Yves 1981- La Harpe, Pierre de |
| author_role | aut aut |
| author_sort | Cornulier, Yves 1981- |
| author_variant | y c yc h p d l hpd hpdl |
| building | Verbundindex |
| bvnumber | BV043850933 |
| classification_rvk | SK 260 |
| collection | ZDB-147-EMB |
| ctrlnum | (OCoLC)964687686 (DE-599)BVBBV043850933 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.4171/166 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nmm a2200000 cb4500</leader><controlfield tag="001">BV043850933</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20240917</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161028s2016 gw |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783037196663</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-03719-666-3</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.4171/166</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)964687686</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043850933</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-19</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 260</subfield><subfield code="0">(DE-625)143227:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Cornulier, Yves</subfield><subfield code="d">1981-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1120024137</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Metric geometry of locally compact groups</subfield><subfield code="b">winner of the 2016 EMS Monograph Award</subfield><subfield code="c">Yves Cornulier, Pierre de la Harpe</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Zürich</subfield><subfield code="b">European Mathematical Society Publishing House</subfield><subfield code="c">[2016]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2016</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (viii, 235 Seiten)</subfield><subfield code="b">Diagramme</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">EMS tracts in mathematics</subfield><subfield code="v">25</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Metrischer Raum</subfield><subfield code="0">(DE-588)4169745-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lokal kompakte Gruppe</subfield><subfield code="0">(DE-588)4168094-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Graduate students and advanced undergraduate students mathematicians who wish some introduction to coarse geometry and locally compact groups.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">left-invariant metrics</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Locally compact groups</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">coarse connectedness</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">compact generation</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">compact presentation</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">metric coarse equivalence</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">quasi-isometry</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">second countability</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">sigma-compactness</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Lokal kompakte Gruppe</subfield><subfield code="0">(DE-588)4168094-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Metrischer Raum</subfield><subfield code="0">(DE-588)4169745-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">La Harpe, Pierre de</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)108064158</subfield><subfield code="4">aut</subfield></datafield><datafield tag="710" ind1="2" ind2=" "><subfield code="a">European Mathematical Society Publishing House ETH-Zentrum SEW A27</subfield><subfield code="0">(DE-588)1066118477</subfield><subfield code="4">pbl</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-3-03719-166-8</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">EMS tracts in mathematics</subfield><subfield code="v">25</subfield><subfield code="w">(DE-604)BV043991716</subfield><subfield code="9">25</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.4171/166</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-147-EMB</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029261250</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.4171/166</subfield><subfield code="l">DE-188</subfield><subfield code="p">ZDB-147-EMB</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.4171/166</subfield><subfield code="l">DE-91</subfield><subfield code="p">ZDB-147-EMB</subfield><subfield code="q">TUM_Serienkauf</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.4171/166</subfield><subfield code="l">DE-19</subfield><subfield code="p">ZDB-147-EMB</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.4171/166</subfield><subfield code="l">DE-355</subfield><subfield code="p">ZDB-147-EMB</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.4171/166</subfield><subfield code="l">DE-703</subfield><subfield code="p">ZDB-147-EMB</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043850933 |
| illustrated | Not Illustrated |
| indexdate | 2024-09-17T14:06:42Z |
| institution | BVB |
| institution_GND | (DE-588)1066118477 |
| isbn | 9783037196663 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029261250 |
| oclc_num | 964687686 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-91 DE-BY-TUM DE-188 DE-355 DE-BY-UBR DE-703 DE-83 DE-11 |
| owner_facet | DE-19 DE-BY-UBM DE-91 DE-BY-TUM DE-188 DE-355 DE-BY-UBR DE-703 DE-83 DE-11 |
| physical | 1 Online-Ressource (viii, 235 Seiten) Diagramme |
| psigel | ZDB-147-EMB ZDB-147-EMB TUM_Serienkauf |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | European Mathematical Society Publishing House |
| record_format | marc |
| series | EMS tracts in mathematics |
| series2 | EMS tracts in mathematics |
| 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 |
| url | https://doi.org/10.4171/166 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 |
| volume_link | (DE-604)BV043991716 |
| work_keys_str_mv | AT cornulieryves metricgeometryoflocallycompactgroupswinnerofthe2016emsmonographaward AT laharpepierrede metricgeometryoflocallycompactgroupswinnerofthe2016emsmonographaward AT europeanmathematicalsocietypublishinghouseethzentrumsewa27 metricgeometryoflocallycompactgroupswinnerofthe2016emsmonographaward |