Verfügbarkeit: Large scale geometry | Technische Universität München

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Bibliographische Detailangaben
Beteiligte Personen:	Nowak, Piotr (VerfasserIn), Yu, Guoliang 1963- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Zürich European Mathematical Soc. 2012
Schriftenreihe:	EMS textbooks in mathematics
Schlagwörter:	Geometry Banach-Raum Hyperbolische Gruppe Metrischer Raum Homologiegruppe Endlich erzeugte Gruppe
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025305447&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XIV, 189 S. graph. Darst.
ISBN:	9783037191125

Internformat

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Datensatz im Suchindex

DE-BY-UBR_call_number	80/SK 350 N946 803/SK 350 N946
DE-BY-UBR_katkey	5022442
DE-BY-UBR_location	UB Lesesaal Mathematik UB Handapparat Mathematik Prof. Ammann
DE-BY-UBR_media_number	069039562692 TEMP12423014
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adam_text	Contents Preface vii Notation and conventions xiii 1 Metric spaces and large scale geometry 1 1.1 Metric spaces . 1 1.2 Groups as metric spaces . 6 1.3 Quasi-isometries . 9 1.4 Coarse equivalences . 15 1.5 Hyperbolic spaces . 19 Exercises . 24 Notes and remarks . 25 2 Asymptotic dimension and decomposition complexity 26 2.1 Topological dimension . 26 2.2 Asymptotic dimension . 27 2.3 Dimension of hyperbolic groups . 30 2.4 Upper bounds for asymptotic dimension . 32 2.5 Asymptotic dimension of solvable groups . 36 2.6 Groups with infinite asymptotic dimension . 38 2.7 Decomposition complexity . 39 2.8 Invariance and permanence . 42 2.9 Groups with finite decomposition complexity . 45 Exercises . 47 Notes and remarks . 47 3 Amenability 49 3.1 F0mer conditions . 49 3.2 The Hulanicki—Reiter condition . . 55 3.3 Invariant means . 58 Exercises . 61 Notes and remarks . 61 4 Property A 63 4.1 Definition and basic properties . 63 4.2 The Higson-Roe condition . 66 4.3 Finite asymptotic dimension implies property A . 70 X Contents 4.4 Property A and residually finite groups . 73 4.5 Locally finite examples . 78 Exercises . 81 Notes and remarks . 81 5 Coarse embeddings 83 5.1 Coarse embeddings . 83 5.2 Embeddability into Hubert spaces . 84 5.3 Examples of embeddable spaces without property A . 89 5.4 Convexity and reflexivity . 91 5.5 Coarse embeddings and finite subsets . 96 5.6 Expanders . 98 5.7 A geometric characterization of non-embeddability . 101 5.8 Compression of coarse embeddings . 108 5.9 Compression > ^ implies property A . 110 Exercises . 116 Notes and remarks . 117 6 Group actions on Banach spaces 119 6.1 Affine isometric actions . 119 6.2 Metrically proper actions and a-T-menability . 121 6.3 Actions on ¿p-spaces and reflexive В anach spaces . 125 6.4 Kazhdan's property (T) . 128 6.5 Fixed points and KajŁhdan' s property (T) . 130 6.6 Construction of expanders .,. 132 6.7 Property (T) and spectral conditions . 134 Exercises . 140 Notes and remarks . 141 7 Coarse homology 143 7.1 Coarse locally finite homology . 143 7.2 Uniformly finite homology . 144 7.3 Eilenberg swindles and Ponzi schemes . 149 7.4 Aperiodic tiles and non-amenable spaces . 154 7.5 Coarsening homology theories . 160 7.6 The coarsening homomorphism . 162 Exercises . 165 Notes and remarks . 165 Contents χι 8 Survey of applications 166 8.1 Topological rigidity . 166 8.2 Geometric rigidity . 167 8.3 Index theory . 169 References 172 Index 187
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isbn	9783037191125
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physical	XIV, 189 S. graph. Darst.
publishDate	2012
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publishDateSort	2012
publisher	European Mathematical Soc.
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series2	EMS textbooks in mathematics
spellingShingle	Nowak, Piotr Yu, Guoliang 1963- Large scale geometry Geometry Banach-Raum (DE-588)4004402-6 gnd Hyperbolische Gruppe (DE-588)4238166-6 gnd Metrischer Raum (DE-588)4169745-5 gnd Homologiegruppe (DE-588)4160597-4 gnd Endlich erzeugte Gruppe (DE-588)4225681-1 gnd
subject_GND	(DE-588)4004402-6 (DE-588)4238166-6 (DE-588)4169745-5 (DE-588)4160597-4 (DE-588)4225681-1
title	Large scale geometry
title_auth	Large scale geometry
title_exact_search	Large scale geometry
title_full	Large scale geometry Piotr W. Nowak ; Guoliang Yu
title_fullStr	Large scale geometry Piotr W. Nowak ; Guoliang Yu
title_full_unstemmed	Large scale geometry Piotr W. Nowak ; Guoliang Yu
title_short	Large scale geometry
title_sort	large scale geometry
topic	Geometry Banach-Raum (DE-588)4004402-6 gnd Hyperbolische Gruppe (DE-588)4238166-6 gnd Metrischer Raum (DE-588)4169745-5 gnd Homologiegruppe (DE-588)4160597-4 gnd Endlich erzeugte Gruppe (DE-588)4225681-1 gnd
topic_facet	Geometry Banach-Raum Hyperbolische Gruppe Metrischer Raum Homologiegruppe Endlich erzeugte Gruppe
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025305447&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT nowakpiotr largescalegeometry AT yuguoliang largescalegeometry

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