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Group colorings and Bernoulli subflows /
In this paper the authors study the dynamics of Bernoulli flows and their subflows over general countable groups. One of the main themes of this paper is to establish the correspondence between the topological and the symbolic perspectives. From the topological perspective, the authors are particula...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
2016.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1141. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title page; Chapter 1. Introduction; 1.1. Bernoulli flows and subflows; 1.2. Basic notions; 1.3. Existence of free subflows; 1.4. Hyper aperiodic points and -colorings; 1.5. Complexity of sets and equivalence relations; 1.6. Tilings of groups; 1.7. The almost equality relation; 1.8. The fundamental method; 1.9. Brief outline; Chapter 2. Preliminaries; 2.1. Bernoulli flows; 2.2. 2-colorings; 2.3. Orthogonality; 2.4. Minimality; 2.5. Strengthening and weakening of 2-colorings; 2.6. Other variations of 2-colorings; 2.7. Subflows of (2 N) G
- Chapter 3. Basic Constructions of 2-Colorings 3.1. 2-Colorings on supergroups of finite index; 3.2. 2-Colorings on group extensions; 3.3. 2-Colorings on Z; 3.4. 2-Colorings on nonabelian free groups; 3.5. 2-Colorings on solvable groups; 3.6. 2-Colorings on residually finite groups; Chapter 4. Marker Structures and Tilings; 4.1. Marker structures on groups; 4.2. 2-Colorings on abelian and FC groups by markers; 4.3. Some properties of \ccc groups; 4.4. Abelian, nilpotent, and polycyclic groups are \ccc; 4.5. Residually finite and locally finite groups and free products are ccc
- Chapter 5. Blueprints and Fundamental Functions5.1. Blueprints; 5.2. Fundamental functions; 5.3. Existence of blueprints; 5.4. Growth of blueprints; Chapter 6. Basic Applications of the Fundamental Method; 6.1. The uniform 2-coloring property; 6.2. Density of 2-colorings; 6.3. Characterization of the ACP; Chapter 7. Further Study of Fundamental Functions; 7.1. Subflows generated by fundamental functions; 7.2. Pre-minimality; 7.3. [Delta]-minimality; 7.4. Minimality constructions; 7.5. Rigidity constructions for topological conjugacy
- Chapter 8. The Descriptive Complexity of Sets of 2-Colorings 8.1. Smallness in measure and category 8.2. [Sigma] 0 2 -hardness and [Pi] 0 2 -completeness 8.3. Flecc groups; 8.4. Nonflecc groups; Chapter 9. The Complexity of the Topological Conjugacy Relation; 9.1. Introduction to countable Borel equivalence relations; 9.2. Basic properties of topological conjugacy; 9.3. Topological conjugacy of minimal free subflows; 9.4. Topological conjugacy of free subflows
- Chapter 10. Extending Partial Functions to 2-Colorings; 10.1. A sufficient condition for extendability; 10.2. A characterization for extendability; 10.3. Almost equality and cofinite domains 10.4. Automatic extendability Chapter 11. Further Questions; 11.1. Group structures; 11.2. 2-colorings; 11.3. Generalizations; 11.4. Descriptive complexity; Bibliography; Index; Back Cover