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Cantor minimal systems

Author: Ian F Putnam
Publisher: Providence, Rhode Island : American Mathematical Society, [2018] ©2018
Series: University lecture series (Providence, R.I.), 70.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Within the subject of topological dynamics, there has been considerable recent interest in systems where the underlying topological space is a Cantor set. Such systems have an inherently combinatorial nature, and seminal ideas of Anatoly Vershik allowed for a combinatorial model, called the Bratteli-Vershik model, for such systems with no non-trivial closed invariant subsets. This model led to a construction of an  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Putnam, Ian F. (Ian Fraser), 1958-
Cantor minimal systems.
Providence, Rhode Island : American Mathematical Society, [2018]
(DLC) 2017057279
(OCoLC)1020292439
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ian F Putnam
ISBN: 9781470447311 1470447312
OCLC Number: 1039345861
Description: 1 online resource : illustrations
Contents: Cover; Title page; Contents; Preface; Chapter 1. An example: A tale of two equivalence relations; Chapter 2. Basics: Cantor sets and orbit equivalence; 1. Cantor sets; 2. Orbit equivalence; Chapter 3. Bratteli diagrams: Generalizing the example; Chapter 4. The Bratteli-Vershik model: Generalizing the example; Chapter 5. The Bratteli-Vershik model: Completeness; Chapter 6. Étale equivalence relations: Unifying the examples; 1. Local actions and étale equivalence relations; 2. _{ } as an étale equivalence relation; 3. _{ } as an étale equivalence relation; Chapter 7. The invariant. 1. The group (, \Z)2. Ordered abelian groups; 3. The invariant; 4. Inductive limits of groups; 5. The dimension group of a Bratteli diagram; 6. The invariant for AF-equivalence relations; 7. The invariant for \Z-actions; Chapter 8. The Effros-Handelman-Shen Theorem; 1. The statement; 2. The proof; Chapter 9. The Bratteli-Elliott-Krieger Theorem; Chapter 10. Strong orbit equivalence; 1. Orbit cocycles; 2. Strong orbit equivalence and classification; Chapter 11. The _{ } invariant; 1. An innocent's guide to measure theory; 2. States on ordered abelian groups; 3.-invariant measures. 4.-invariant measures and the invariant5. The invariant; 6. The invariant for AF-equivalence relations; 7. The invariant for \Z-actions; 8. The classification of odometers; Chapter 12. The absorption theorem; 1. The simplest version; 2. The proof; 3. Matui's absorption theorem; Chapter 13. The classification of AF-equivalence relations; 1. An example; 2. The classification theorem; Chapter 14. The classification of \Z-actions; Appendix A. Examples; Bibliography; Index of terminology; Index of notation; Back Cover.
Series Title: University lecture series (Providence, R.I.), 70.
Responsibility: Ian F. Putnam.

Abstract:

Within the subject of topological dynamics, there has been considerable recent interest in systems where the underlying topological space is a Cantor set. Such systems have an inherently combinatorial nature, and seminal ideas of Anatoly Vershik allowed for a combinatorial model, called the Bratteli-Vershik model, for such systems with no non-trivial closed invariant subsets. This model led to a construction of an ordered abelian group which is an algebraic invariant of the system providing a complete classification of such systems up to orbit equivalence. The goal of this book is to give a st.

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