Group colorings and Bernoulli subflows:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
May 2016
|
| Series: | Memoirs of the American Mathematical Society
volume 241, number 1141 (2nd of 4 numbers) |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | vi, 241 Seiten |
| ISBN: | 9781470418472 |
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MARC
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Record in the Search Index
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| adam_text | Contents
Chapter 1. Introduction 1
1.1. Bernoulli flows and subflows 1
1.2. Basic notions 3
1.3. Existence of free subflows 4
1.4. Hyper aperiodic points and fc-colorings 6
1.5. Complexity of sets and equivalence relations 9
1.6. Tilings of groups 11
1.7. The almost equality relation 12
1.8. The fundamental method 14
1.9. Brief outline 16
Chapter 2. Preliminaries 19
2.1. Bernoulli flows 19
2.2. 2-colorings 21
2.3. Orthogonality 23
2.4. Minimality 24
2.5. Strengthening and weakening of 2-colorings 27
2.6. Other variations of 2-colorings 30
2.7. Subflows of (2n) 7 32
Chapter 3. Basic Constructions of 2-Colorings 35
3.1. 2-Colorings on supergroups of finite index 35
3.2. 2-Colorings on group extensions 39
3.3. 2-Colorings on Z 43
3.4. 2-Colorings on nonabelian free groups 46
3.5. 2-Colorings on solvable groups 48
3.6. 2-Colorings on residually finite groups 51
Chapter 4. Marker Structures and Tilings 53
4.1. Marker structures on groups 53
4.2. 2-Colorings on abelian and FC groups by markers 57
4.3. Some properties of ccc groups 61
4.4. Abelian, nilpotent. and polycyclic groups are ccc 63
4.5. Residually finite and locally finite groups and free products are ccc 70
Chapter 5. Blueprints and Fundamental Functions 77
5.1. Blueprints 77
5.2. Fundamental functions 84
5.3. Existence of blueprints 91
5.4. Growth of blueprints 98
iii
IV
CONTENTS
Chapter 6. Basic Applications of the Fundamental Method 103
6.1. The uniform 2-coloring property 103
6.2. Density of 2-colorings 107
6.3. Characterization of the ACP 109
Chapter 7. Further Study of Fundamental Functions 117
7.1. Subflows generated by fundamental functions 117
7.2. Pre-minimality 122
7.3. A-minimality 127
7.4. Minimality constructions * 131
7.5. Rigidity constructions for topological conjugacy 138
Chapter 8. The Descriptive Complexity of Sets of 2-Colorings 147
8.1. Smallness in measure and category 147
8.2. -hardness and JT§-completeness 148
8.3. Flecc groups 151
8.4. Nonflecc groups 156
Chapter 9. The Complexity of the Topological Conjugacy Relation 169
9.1. Introduction to countable Borel equivalence relations 169
9.2. Basic properties of topological conjugacy 170
9.3. Topological conjugacy of minimal free subflows 176
9.4. Topological conjugacy of free subflows 185
Chapter 10. Extending Partial Functions to 2-Colorings 205
10.1. A sufficient condition for extendability 205
10.2. A characterization for extendability 207
10.3. Almost equality and cofinite domains 218
10.4. Automatic extendability 229
Chapter 11. Further Questions 233
11.1. Group structures 233
11.2. 2-colorings 234
11.3. Generalizations 235
11.4. Descriptive complexity 236
Bibliography 237
Index 239
|
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| indexdate | 2024-07-10T07:28:50Z |
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| isbn | 9781470418472 |
| language | English |
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| physical | vi, 241 Seiten |
| publishDate | 2016 |
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| publishDateSort | 2016 |
| publisher | American Mathematical Society |
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| series2 | Memoirs of the American Mathematical Society |
| spelling | Gao, Su 1968- (DE-588)173594093 aut Group colorings and Bernoulli subflows Su Gao, Steve Jackson, Brandon Seward Providence, Rhode Island American Mathematical Society May 2016 vi, 241 Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 241, number 1141 (2nd of 4 numbers) Hydromechanik (DE-588)4026312-5 gnd rswk-swf Hydromechanik (DE-588)4026312-5 s DE-604 Jackson, Steve 1957- (DE-588)138594686 aut Seward, Brandon 1987- (DE-588)1098578724 aut Memoirs of the American Mathematical Society volume 241, number 1141 (2nd of 4 numbers) (DE-604)BV008000141 1141 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=028973894&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gao, Su 1968- Jackson, Steve 1957- Seward, Brandon 1987- Group colorings and Bernoulli subflows Memoirs of the American Mathematical Society Hydromechanik (DE-588)4026312-5 gnd |
| subject_GND | (DE-588)4026312-5 |
| title | Group colorings and Bernoulli subflows |
| title_auth | Group colorings and Bernoulli subflows |
| title_exact_search | Group colorings and Bernoulli subflows |
| title_full | Group colorings and Bernoulli subflows Su Gao, Steve Jackson, Brandon Seward |
| title_fullStr | Group colorings and Bernoulli subflows Su Gao, Steve Jackson, Brandon Seward |
| title_full_unstemmed | Group colorings and Bernoulli subflows Su Gao, Steve Jackson, Brandon Seward |
| title_short | Group colorings and Bernoulli subflows |
| title_sort | group colorings and bernoulli subflows |
| topic | Hydromechanik (DE-588)4026312-5 gnd |
| topic_facet | Hydromechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028973894&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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