Large scale geometry:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Zürich
European Mathematical Soc.
2012
|
| Series: | EMS textbooks in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 189 S. graph. Darst. |
| ISBN: | 9783037191125 |
Staff View
MARC
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| 100 | 1 | |a Nowak, Piotr |e Verfasser |0 (DE-588)141626224 |4 aut | |
| 245 | 1 | 0 | |a Large scale geometry |c Piotr W. Nowak ; Guoliang Yu |
| 264 | 1 | |a Zürich |b European Mathematical Soc. |c 2012 | |
| 300 | |a XIV, 189 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
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Record in the Search Index
| _version_ | 1815793575369113600 |
|---|---|
| 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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| author | Nowak, Piotr Yu, Guoliang 1963- |
| author_GND | (DE-588)141626224 (DE-588)1026997461 |
| author_facet | Nowak, Piotr Yu, Guoliang 1963- |
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| author_sort | Nowak, Piotr |
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| building | Verbundindex |
| bvnumber | BV040457943 |
| classification_rvk | SK 350 SK 380 |
| ctrlnum | (OCoLC)815944522 (DE-599)BVBBV040457943 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV040457943 |
| illustrated | Illustrated |
| indexdate | 2024-11-15T13:01:36Z |
| institution | BVB |
| isbn | 9783037191125 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025305447 |
| oclc_num | 815944522 |
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| physical | XIV, 189 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | European Mathematical Soc. |
| record_format | marc |
| series2 | EMS textbooks in mathematics |
| spelling | Nowak, Piotr Verfasser (DE-588)141626224 aut Large scale geometry Piotr W. Nowak ; Guoliang Yu Zürich European Mathematical Soc. 2012 XIV, 189 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier EMS textbooks in mathematics Geometry Banach-Raum (DE-588)4004402-6 gnd rswk-swf Hyperbolische Gruppe (DE-588)4238166-6 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Homologiegruppe (DE-588)4160597-4 gnd rswk-swf Endlich erzeugte Gruppe (DE-588)4225681-1 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s Endlich erzeugte Gruppe (DE-588)4225681-1 s Homologiegruppe (DE-588)4160597-4 s Hyperbolische Gruppe (DE-588)4238166-6 s Metrischer Raum (DE-588)4169745-5 s 1\p DE-604 Yu, Guoliang 1963- Verfasser (DE-588)1026997461 aut Erscheint auch als Online-Ausgabe 978-3-03719-612-0 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf 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 Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| 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 |