Lectures on coarse geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematcal Society
[2003]
|
| Series: | University lecture series
Volume 31 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | vii, 175 Seiten Diagramme |
| ISBN: | 0821833324 9780821833322 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface vii
Chapter 1. Metric Spaces 1
1.1. Legendre on hyperbolic geometry 1
1.2. Metric spaces and length spaces 3
1.3. The coarse perspective on metric spaces 5
1.4. Groups and leaves 7
1.5. Trees and complexes 11
1.6. Hyperbolic space 13
1.7. Nilpotent examples — Heisenberg group 18
Chapter 2. Coarse Spaces 21
2.1. The abstract notion of coarse structure 21
2.2. Topological coarse structure 26
2.3. The Higson corona 29
2.4. Metrization of coarse structures 33
2.5. Hyperbolization 35
Chapter 3. Growth and amenability 39
3.1. Bounded geometry 39
3.2. Growth 42
3.3. Amenable spaces 44
3.4. Examples of amenable and nonamenable spaces 47
3.5. Amenable groups 51
3.6. F0lner s Theorem 55
3.7. Amenability and analysis 58
Chapter 4. Translation Algebras 59
4.1. Translation Algebras 59
4.2. Amenability and the Translation Algebra 60
4.3. Finiteness of Group Algebras 63
4.4. Translation C* Algebras 66
4.5. Translation Algebras as Crossed Products 68
Chapter 5. Coarse Algebraic Topology 71
5.1. Coarse cohomology theory 71
5.2. Product structure on coarse theory 76
5.3. Computation of coarse cohomology 78
V
vi CONTENTS
5.4. Covers, nerves and metrization 80
5.5. Coarse homology theories 82
5.6. The Coarse Baum Connes conjecture 84
Chapter 6. Coarse Negative Curvature 87
6.1. Curvature conditions 87
6.2. The Rips property and Gromov hyperbolicity 88
6.3. Controlling quasigeodesics 92
6.4. The Gromov boundary of a hyperbolic space 93
6.5. Bolicity 97
Chapter 7. Limits of Metric Spaces 99
7.1. Convergence of metric spaces 99
7.2. The rescaled limit of metric spaces 101
7.3. Groups of polynomial growth l04
7.4. Ultralimits 105
7.5. Asymptotic Cones 107
Chapter 8. Rigidity in
8.1. What is rigidity? 111
8.2. The quasi isometry group of hyperbolic space 112
8.3. Proof of Mostow Rigidity 117
8.4. Quasi Isometric Rigidity For Products of Hyperbolic Spaces 121
Chapter 9. Asymptotic Dimension 129
9.1. The asymptotic dimension of a coarse space 129
9.2. Composition properties of asymptotic dimension 132
9.3. More Examples 136
9.4. Analytic implications of finite asymptotic dimension I39
Chapter 10. Groupoids and coarse geometry 141
10.1. Reminders about topological groupoids 141
10.2. The pair product and the Stone Cech boundary 143
10.3. The translation groupoid of a coarse space
10.4. Translation groupoid and translation algebra 148
Chapter 11. Coarse Embeddability 151
11.1. Coarse embedding 151
11.2. Kernels and embeddings in Hilbert space 153
11.3. Embeddability and Property T 157
11.4. Property T and coarse equivalence 162
11.5. Property A and exactness for group C* algebras 165
Bibliography 173
|
| any_adam_object | 1 |
| author | Roe, John 1959- |
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| dewey-full | 514/.325 514.325 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.325 514.325 |
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| dewey-sort | 3514 3325 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV017428358 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:17:54Z |
| institution | BVB |
| isbn | 0821833324 9780821833322 |
| language | English |
| lccn | 2003052385 |
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| physical | vii, 175 Seiten Diagramme |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | American Mathematcal Society |
| record_format | marc |
| series | University lecture series |
| series2 | University lecture series |
| spelling | Roe, John 1959- Verfasser (DE-588)172334810 aut Lectures on coarse geometry John Roe Providence, Rhode Island American Mathematcal Society [2003] © 2003 vii, 175 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier University lecture series Volume 31 Differentiaalmeetkunde gtt Algebraic topology Metric spaces Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 s Algebraische Topologie (DE-588)4120861-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2176-2 University lecture series Volume 31 (DE-604)BV004153846 31 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010501547&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roe, John 1959- Lectures on coarse geometry University lecture series Differentiaalmeetkunde gtt Algebraic topology Metric spaces Algebraische Topologie (DE-588)4120861-4 gnd Metrischer Raum (DE-588)4169745-5 gnd |
| subject_GND | (DE-588)4120861-4 (DE-588)4169745-5 |
| title | Lectures on coarse geometry |
| title_auth | Lectures on coarse geometry |
| title_exact_search | Lectures on coarse geometry |
| title_full | Lectures on coarse geometry John Roe |
| title_fullStr | Lectures on coarse geometry John Roe |
| title_full_unstemmed | Lectures on coarse geometry John Roe |
| title_short | Lectures on coarse geometry |
| title_sort | lectures on coarse geometry |
| topic | Differentiaalmeetkunde gtt Algebraic topology Metric spaces Algebraische Topologie (DE-588)4120861-4 gnd Metrischer Raum (DE-588)4169745-5 gnd |
| topic_facet | Differentiaalmeetkunde Algebraic topology Metric spaces Algebraische Topologie Metrischer Raum |
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| work_keys_str_mv | AT roejohn lecturesoncoarsegeometry |