Overview
- Provides a solid introduction to the theory of topological dynamics and crossed products
- Contains a large collection of examples and explicit computations
- Shows developments in topological orbit equivalence, particularly treating the classification of minimal actions of finitely generated abelian groups on the Cantor set
Part of the book series: Advanced Courses in Mathematics - CRM Barcelona (ACMBIRK)
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Table of contents (25 chapters)
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Front Matter
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The Cuntz Semigroup and the Classification of C*-Algebras
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Front Matter
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An Introduction to Crossed Product C*-Algebras and Minimal Dynamics
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Front Matter
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C*-Algebras and Topological Dynamics: Finite Approximation and Paradoxicality
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Front Matter
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Keywords
About this book
This book collects the notes of the lectures given at an Advanced Course on Dynamical Systems at the Centre de Recerca Matemàtica (CRM) in Barcelona. The notes consist of four series of lectures.
The first one, given by Andrew Toms, presents the basic properties of the Cuntz semigroup and its role in the classification program of simple, nuclear, separable C*-algebras. The second series of lectures, delivered by N. Christopher Phillips, serves as an introduction to group actions on C*-algebras and their crossed products, with emphasis on the simple case and when the crossed products are classifiable. The third one, given by David Kerr, treats various developments related to measure-theoretic and topological aspects of crossed products, focusing on internal and external approximation concepts, both for groups and C*-algebras. Finally, the last series of lectures, delivered by Thierry Giordano, is devoted to the theory of topological orbit equivalence, with particular attentionto the classification of minimal actions by finitely generated abelian groups on the Cantor set.
Authors, Editors and Affiliations
About the editor
Thierry Giordano is a Professor at the University of Ottawa, Canada.
David Kerr is a Professor at the Texas A&M University in College Station, TX, USA.
N. Christopher Phillips is a Professor at the University of Oregon in Eugene, OR, USA.
Andrew S. Toms is a Professor at the Purdue University in West Lafayette, IN, USA.
Bibliographic Information
Book Title: Crossed Products of C*-Algebras, Topological Dynamics, and Classification
Authors: Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
Editors: Francesc Perera
Series Title: Advanced Courses in Mathematics - CRM Barcelona
DOI: https://doi.org/10.1007/978-3-319-70869-0
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Softcover ISBN: 978-3-319-70868-3Published: 06 September 2018
eBook ISBN: 978-3-319-70869-0Published: 28 August 2018
Series ISSN: 2297-0304
Series E-ISSN: 2297-0312
Edition Number: 1
Number of Pages: X, 498
Topics: Functional Analysis