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...

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Bibliographic Details
Main Authors: Guentner, Erik, 1965- (Author), Willett, Rufus, 1983- (Author), Yu, Guoliang, 1963- (Author)
Format: Book
Language:English
Language Notes:Abstracts in English and in French.
Published: Paris : Société mathématique de France, 2024.
Series:Astérisque ; 451.
Subjects:
Description
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.
Physical Description:89 pages ; 24 cm.
Bibliography:Includes bibliographical references.
ISBN:9782379052026
2379052026