Dynamical complexity and controlled operator K-theory /
In this volume, we introduce a property of topological dynamical systems that we call finite dynamical complexity. For systems with this property, one can in principle compute the K-theory of the associated crossed product C*-algebra by splitting it up into simpler pieces and using the methods of co...
| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Language Notes: | Abstracts in English and in French. |
| Published: |
Paris :
Société mathématique de France,
2024.
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| Series: | Astérisque ;
451. |
| Subjects: |
| Summary: | In this volume, we introduce a property of topological dynamical systems that we call finite dynamical complexity. For systems with this property, one can in principle compute the K-theory of the associated crossed product C*-algebra by splitting it up into simpler pieces and using the methods of controlled K-theory. The main part of the paper illustrates this idea by giving a new proof of the Baum-Connes conjecture for actions with finite dynamical complexity. We have tried to keep the paper as self-contained as possible: we hope the main part will be accessible to someone with the equivalent of a first course in operator K-theory. In particular, we do not assume prior knowledge of controlled K-theory, and use a new and concrete model for the Baum-Connes conjecture with coefficients that requires no bivariant K-theory to set up. |
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| Physical Description: | 89 pages ; 24 cm. |
| Bibliography: | Includes bibliographical references. |
| ISBN: | 9782379052026 2379052026 |