Large scale geometry:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
EMS Press
[2023]
|
| Ausgabe: | Second edition |
| Schriftenreihe: | EMS Textbooks in Mathematics
26 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xvi, 197 Seiten Diagramme 23.5 cm x 16.5 cm |
| ISBN: | 3985470189 9783985470181 |
Internformat
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 |
| 250 | |a Second edition | ||
| 264 | 1 | |a Berlin |b EMS Press |c [2023] | |
| 264 | 4 | |c ©2023 | |
| 300 | |a xvi, 197 Seiten |b Diagramme |c 23.5 cm x 16.5 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a EMS Textbooks in Mathematics |v 26 | |
| 630 | 0 | 4 | |a Geometry |
| 650 | 0 | 7 | |a Banach-Raum |0 (DE-588)4004402-6 |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 Metrische Geometrie |0 (DE-588)4278656-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Grobstruktur |0 (DE-588)4519326-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Homologiegruppe |0 (DE-588)4160597-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Endlich erzeugte Gruppe |0 (DE-588)4225681-1 |2 gnd |9 rswk-swf |
| 653 | |a Baum–Connes conjecture | ||
| 653 | |a Borel conjecture | ||
| 653 | |a Novikov conjecture | ||
| 653 | |a Property A | ||
| 653 | |a a-T-menability | ||
| 653 | |a amenability | ||
| 653 | |a asymptotic dimension | ||
| 653 | |a coarse Baum–Connes conjecture | ||
| 653 | |a coarse embedding | ||
| 653 | |a coarse geometry | ||
| 653 | |a coarse homology | ||
| 653 | |a expanders | ||
| 653 | |a finite decomposition complexity | ||
| 653 | |a large scale geometry | ||
| 653 | |a quasi-isometry | ||
| 653 | |a uniformly finite homology | ||
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Datensatz im Suchindex
| _version_ | 1815793575378550784 |
|---|---|
| adam_text |
CONTENTS
PREFACE
.
VII
NOTATION
AND
CONVENTIONS
.
XV
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
.
27
2.1
TOPOLOGICAL
DIMENSION
.
27
2.2
ASYMPTOTIC
DIMENSION
.
28
2.3
DIMENSION
OF
HYPERBOLIC
GROUPS
.
31
2.4
UPPER
BOUNDS
FOR
ASYMPTOTIC
DIMENSION
.
33
2.5
ASYMPTOTIC
DIMENSION
OF
SOLVABLE
GROUPS
.
37
2.6
GROUPS
WITH
INFINITE
ASYMPTOTIC
DIMENSION
.
39
2.7
DECOMPOSITION
COMPLEXITY
.
40
2.8
INVARIANCE
AND
PERMANENCE
.
43
2.9
GROUPS
WITH
FINITE
DECOMPOSITION
COMPLEXITY
.
46
EXERCISES
.
48
NOTES
AND
REMARKS
.
48
3
AMENABILITY
.
51
3.1
F01NER
CONDITIONS
.
51
3.2
THE
HULANICKI-REITER
CONDITION
.
57
3.3
INVARIANT
MEANS
.
60
EXERCISES
.
62
NOTES
AND
REMARKS
.
63
4
PROPERTY
A
.
65
4.1
DEFINITION
AND
BASIC
PROPERTIES
.
65
4.2
THE
HIGSON-ROE
CONDITION
.
68
XII
CONTENTS
4.3
FINITE
ASYMPTOTIC
DIMENSION
IMPLIES
PROPERTY
A
.
72
4.4
PROPERTY
A
AND
RESIDUALLY
FINITE
GROUPS
.
76
4.5
LOCALLY
FINITE
EXAMPLES
.
80
EXERCISES
.
84
NOTES
AND
REMARKS
.
84
5
COARSE
EMBEDDINGS
.
87
5.1
COARSE
EMBEDDINGS
.
87
5.2
EMBEDDABILITY
INTO
HILBERT
SPACES
.
88
5.3
EXAMPLES
OF
EMBEDDABLE
SPACES
WITHOUT
PROPERTY
A
.
93
5.4
CONVEXITY
AND
REFLEXIVITY
.
95
5.5
COARSE
EMBEDDINGS
AND
FINITE
SUBSETS
.
100
5.6
EXPANDERS
.
102
5.7
A
GEOMETRIC
CHARACTERIZATION
OF
NON-EMBEDDABILITY
.
105
5.8
COMPRESSION
OF
COARSE
EMBEDDINGS
.
112
5.9
COMPRESSION
3
IMPLIES
PROPERTY
A
.
114
EXERCISES
.
120
NOTES
AND
REMARKS
.
121
6
GROUP
ACTIONS
ON
BANACH
SPACES
.
123
6.1
AFFINE
ISOMETRIC
ACTIONS
.
123
6.2
METRICALLY
PROPER
ACTIONS
AND
A-T-MENABILITY
.
125
6.3
ACTIONS
ON
EP-SPACES
AND
REFLEXIVE
BANACH
SPACES
.
129
6.4
KAZHDAN
'
S
PROPERTY
(T)
.
133
6.5
FIXED
POINTS
AND
KAZHDAN
'
S
PROPERTY
(T)
.
134
6.6
CONSTRUCTION
OF
EXPANDERS
.
136
6.7
PROPERTY
(T)
AND
SPECTRAL
CONDITIONS
.
138
EXERCISES
.
144
NOTES
AND
REMARKS
.
145
7
COARSE
HOMOLOGY
.
147
7.1
COARSE
LOCALLY
FINITE
HOMOLOGY
.
147
7.2
UNIFORMLY
FINITE
HOMOLOGY
.
148
7.3
EILENBERG
SWINDLES
AND
PONZI
SCHEMES
.
153
7.4
APERIODIC
TILES
AND
NON-AMENABLE
SPACES
.
158
7.5
COARSENING
HOMOLOGY
THEORIES
.
164
7.6
THE
COARSENING
HOMOMORPHISM
.
166
EXERCISES
.
168
NOTES
AND
REMARKS
.
169
CONTENTS
XIII
8
SURVEY
OF
APPLICATIONS
.
171
8.1
TOPOLOGICAL
RIGIDITY
.
171
8.2
GEOMETRIC
RIGIDITY
.
172
8.3
INDEX
THEORY
.
174
REFERENCES
.
179
INDEX
.
195 |
| adam_txt |
CONTENTS
PREFACE
.
VII
NOTATION
AND
CONVENTIONS
.
XV
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
.
27
2.1
TOPOLOGICAL
DIMENSION
.
27
2.2
ASYMPTOTIC
DIMENSION
.
28
2.3
DIMENSION
OF
HYPERBOLIC
GROUPS
.
31
2.4
UPPER
BOUNDS
FOR
ASYMPTOTIC
DIMENSION
.
33
2.5
ASYMPTOTIC
DIMENSION
OF
SOLVABLE
GROUPS
.
37
2.6
GROUPS
WITH
INFINITE
ASYMPTOTIC
DIMENSION
.
39
2.7
DECOMPOSITION
COMPLEXITY
.
40
2.8
INVARIANCE
AND
PERMANENCE
.
43
2.9
GROUPS
WITH
FINITE
DECOMPOSITION
COMPLEXITY
.
46
EXERCISES
.
48
NOTES
AND
REMARKS
.
48
3
AMENABILITY
.
51
3.1
F01NER
CONDITIONS
.
51
3.2
THE
HULANICKI-REITER
CONDITION
.
57
3.3
INVARIANT
MEANS
.
60
EXERCISES
.
62
NOTES
AND
REMARKS
.
63
4
PROPERTY
A
.
65
4.1
DEFINITION
AND
BASIC
PROPERTIES
.
65
4.2
THE
HIGSON-ROE
CONDITION
.
68
XII
CONTENTS
4.3
FINITE
ASYMPTOTIC
DIMENSION
IMPLIES
PROPERTY
A
.
72
4.4
PROPERTY
A
AND
RESIDUALLY
FINITE
GROUPS
.
76
4.5
LOCALLY
FINITE
EXAMPLES
.
80
EXERCISES
.
84
NOTES
AND
REMARKS
.
84
5
COARSE
EMBEDDINGS
.
87
5.1
COARSE
EMBEDDINGS
.
87
5.2
EMBEDDABILITY
INTO
HILBERT
SPACES
.
88
5.3
EXAMPLES
OF
EMBEDDABLE
SPACES
WITHOUT
PROPERTY
A
.
93
5.4
CONVEXITY
AND
REFLEXIVITY
.
95
5.5
COARSE
EMBEDDINGS
AND
FINITE
SUBSETS
.
100
5.6
EXPANDERS
.
102
5.7
A
GEOMETRIC
CHARACTERIZATION
OF
NON-EMBEDDABILITY
.
105
5.8
COMPRESSION
OF
COARSE
EMBEDDINGS
.
112
5.9
COMPRESSION
3
IMPLIES
PROPERTY
A
.
114
EXERCISES
.
120
NOTES
AND
REMARKS
.
121
6
GROUP
ACTIONS
ON
BANACH
SPACES
.
123
6.1
AFFINE
ISOMETRIC
ACTIONS
.
123
6.2
METRICALLY
PROPER
ACTIONS
AND
A-T-MENABILITY
.
125
6.3
ACTIONS
ON
EP-SPACES
AND
REFLEXIVE
BANACH
SPACES
.
129
6.4
KAZHDAN
'
S
PROPERTY
(T)
.
133
6.5
FIXED
POINTS
AND
KAZHDAN
'
S
PROPERTY
(T)
.
134
6.6
CONSTRUCTION
OF
EXPANDERS
.
136
6.7
PROPERTY
(T)
AND
SPECTRAL
CONDITIONS
.
138
EXERCISES
.
144
NOTES
AND
REMARKS
.
145
7
COARSE
HOMOLOGY
.
147
7.1
COARSE
LOCALLY
FINITE
HOMOLOGY
.
147
7.2
UNIFORMLY
FINITE
HOMOLOGY
.
148
7.3
EILENBERG
SWINDLES
AND
PONZI
SCHEMES
.
153
7.4
APERIODIC
TILES
AND
NON-AMENABLE
SPACES
.
158
7.5
COARSENING
HOMOLOGY
THEORIES
.
164
7.6
THE
COARSENING
HOMOMORPHISM
.
166
EXERCISES
.
168
NOTES
AND
REMARKS
.
169
CONTENTS
XIII
8
SURVEY
OF
APPLICATIONS
.
171
8.1
TOPOLOGICAL
RIGIDITY
.
171
8.2
GEOMETRIC
RIGIDITY
.
172
8.3
INDEX
THEORY
.
174
REFERENCES
.
179
INDEX
.
195 |
| any_adam_object | 1 |
| any_adam_object_boolean | 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 | BV049298024 |
| classification_rvk | SK 350 SK 380 |
| ctrlnum | (OCoLC)1410939477 (DE-599)DNB1297549945 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV049298024 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T22:38:33Z |
| indexdate | 2024-11-15T13:01:36Z |
| institution | BVB |
| institution_GND | (DE-588)1066118477 |
| isbn | 3985470189 9783985470181 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034559320 |
| oclc_num | 1410939477 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | xvi, 197 Seiten Diagramme 23.5 cm x 16.5 cm |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | EMS Press |
| record_format | marc |
| series2 | EMS Textbooks in Mathematics |
| spelling | Nowak, Piotr Verfasser (DE-588)141626224 aut Large scale geometry Piotr W. Nowak, Guoliang Yu Second edition Berlin EMS Press [2023] ©2023 xvi, 197 Seiten Diagramme 23.5 cm x 16.5 cm txt rdacontent n rdamedia nc rdacarrier EMS Textbooks in Mathematics 26 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 Metrische Geometrie (DE-588)4278656-3 gnd rswk-swf Grobstruktur (DE-588)4519326-5 gnd rswk-swf Homologiegruppe (DE-588)4160597-4 gnd rswk-swf Endlich erzeugte Gruppe (DE-588)4225681-1 gnd rswk-swf Baum–Connes conjecture Borel conjecture Novikov conjecture Property A a-T-menability amenability asymptotic dimension coarse Baum–Connes conjecture coarse embedding coarse geometry coarse homology expanders finite decomposition complexity large scale geometry quasi-isometry uniformly finite homology 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 DE-604 Grobstruktur (DE-588)4519326-5 s Metrische Geometrie (DE-588)4278656-3 s Yu, Guoliang 1963- Verfasser (DE-588)1026997461 aut European Mathematical Society Publishing House ETH-Zentrum SEW A27 (DE-588)1066118477 pbl Erscheint auch als Online-Ausgabe 978-3-98547-518-6 Vorangegangen ist 1. Auflage 978-3-03719-112-5 (DE-604)BV040457943 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034559320&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20230728 DE-101 https://d-nb.info/provenance/plan#vlb |
| 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 Metrische Geometrie (DE-588)4278656-3 gnd Grobstruktur (DE-588)4519326-5 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)4278656-3 (DE-588)4519326-5 (DE-588)4160597-4 (DE-588)4225681-1 |
| title | Large scale geometry |
| title_auth | Large scale geometry |
| title_exact_search | Large scale geometry |
| title_exact_search_txtP | 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 Metrische Geometrie (DE-588)4278656-3 gnd Grobstruktur (DE-588)4519326-5 gnd Homologiegruppe (DE-588)4160597-4 gnd Endlich erzeugte Gruppe (DE-588)4225681-1 gnd |
| topic_facet | Geometry Banach-Raum Hyperbolische Gruppe Metrischer Raum Metrische Geometrie Grobstruktur Homologiegruppe Endlich erzeugte Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034559320&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nowakpiotr largescalegeometry AT yuguoliang largescalegeometry AT europeanmathematicalsocietypublishinghouseethzentrumsewa27 largescalegeometry |