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Crossed Products of C*-Algebras, Topological Dynamics, and Classification

  • Thierry Giordano
  • David Kerr
  • N. Christopher Phillips
  • Andrew Toms
  • Francesc Perera

Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)

Table of contents

  1. Front Matter
    Pages i-x
  2. The Cuntz Semigroup and the Classification of C*-Algebras

    1. Front Matter
      Pages 1-1
    2. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 3-4
    3. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 5-10
    4. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 11-15
    5. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 17-20
    6. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 21-27
    7. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 29-37
  3. An Introduction to Crossed Product C*-Algebras and Minimal Dynamics

    1. Front Matter
      Pages 39-39
    2. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 41-50
    3. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 51-91
    4. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 93-167
    5. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 169-220
    6. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 221-274
    7. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 275-347
  4. C*-Algebras and Topological Dynamics: Finite Approximation and Paradoxicality

    1. Front Matter
      Pages 349-349
    2. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 351-359
    3. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 361-380
    4. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 381-392
    5. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 393-411
    6. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 413-431
  5. Minimal Topological Systems and Orbit Equivalence

    1. Front Matter
      Pages 433-433
    2. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 435-436
    3. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 437-444
    4. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 445-462
    5. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 463-466
    6. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 467-469
    7. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 471-478
    8. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 479-483
    9. Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
      Pages 485-498

About this book

Introduction

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 attention to the classification of minimal actions by finitely generated abelian groups on the Cantor set.

Keywords

Cuntz semigroup topological dynamics crossed products approximation paradoxicality

Authors and affiliations

  • Thierry Giordano
    • 1
  • David Kerr
    • 2
  • N. Christopher Phillips
    • 3
  • Andrew Toms
    • 4
  1. 1.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada
  2. 2.Department of MathematicsTexas A&M UniversityCollege StationUSA
  3. 3.Department of MathematicsUniversity of OregonEugeneUSA
  4. 4.Department of MathematicsPurdue UniversityWest LafayetteUSA

Editors and affiliations

  • Francesc Perera
    • 1
  1. 1.Universitat Autònoma de BarcelonaDepartament de Matemàtiques Universitat Autònoma de BarcelonaBellaterraSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-70869-0
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-70868-3
  • Online ISBN 978-3-319-70869-0
  • Series Print ISSN 2297-0304
  • Series Online ISSN 2297-0312
  • Buy this book on publisher's site
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