Large scale geometry:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Zürich
European Mathematical Soc.
2012
|
| Schriftenreihe: | EMS textbooks in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 189 S. graph. Darst. |
| ISBN: | 9783037191125 |
Internformat
MARC
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|---|---|---|---|
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| 007 | t | ||
| 008 | 121008s2012 d||| |||| 00||| eng d | ||
| 020 | |a 9783037191125 |c Print |9 978-3-03719-112-5 | ||
| 035 | |a (OCoLC)815944522 | ||
| 035 | |a (DE-599)BVBBV040457943 | ||
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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 | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a EMS textbooks in mathematics | |
| 630 | 0 | 4 | |a Geometry |
| 650 | 0 | 7 | |a Homologiegruppe |0 (DE-588)4160597-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hyperbolische Gruppe |0 (DE-588)4238166-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Metrischer Raum |0 (DE-588)4169745-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Endlich erzeugte Gruppe |0 (DE-588)4225681-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Banach-Raum |0 (DE-588)4004402-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Banach-Raum |0 (DE-588)4004402-6 |D s |
| 689 | 0 | 1 | |a Endlich erzeugte Gruppe |0 (DE-588)4225681-1 |D s |
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| 689 | 0 | 3 | |a Hyperbolische Gruppe |0 (DE-588)4238166-6 |D s |
| 689 | 0 | 4 | |a Metrischer Raum |0 (DE-588)4169745-5 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-025305447 | ||
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Datensatz im Suchindex
| _version_ | 1804149521656053760 |
|---|---|
| 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
|
| any_adam_object | 1 |
| author | Nowak, Piotr Yu, Guoliang 1963- |
| author_GND | (DE-588)141626224 (DE-588)1026997461 |
| author_facet | Nowak, Piotr Yu, Guoliang 1963- |
| author_role | aut aut |
| author_sort | Nowak, Piotr |
| author_variant | p n pn g y gy |
| 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 | 2024-07-10T00:24:21Z |
| 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 Homologiegruppe (DE-588)4160597-4 gnd rswk-swf Hyperbolische Gruppe (DE-588)4238166-6 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Endlich erzeugte Gruppe (DE-588)4225681-1 gnd rswk-swf Banach-Raum (DE-588)4004402-6 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 Homologiegruppe (DE-588)4160597-4 gnd Hyperbolische Gruppe (DE-588)4238166-6 gnd Metrischer Raum (DE-588)4169745-5 gnd Endlich erzeugte Gruppe (DE-588)4225681-1 gnd Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4160597-4 (DE-588)4238166-6 (DE-588)4169745-5 (DE-588)4225681-1 (DE-588)4004402-6 |
| 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 Homologiegruppe (DE-588)4160597-4 gnd Hyperbolische Gruppe (DE-588)4238166-6 gnd Metrischer Raum (DE-588)4169745-5 gnd Endlich erzeugte Gruppe (DE-588)4225681-1 gnd Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Geometry Homologiegruppe Hyperbolische Gruppe Metrischer Raum Endlich erzeugte Gruppe Banach-Raum |
| 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 |