Dynamical complexity and controlled operator K-theory

• Verfasst von: Guentner, Erik [VerfasserIn]
• Verfasst von: Willett, Rufus [VerfasserIn]
• Verfasst von: Yu, Guoliang [VerfasserIn]
• Titel: Dynamical complexity and controlled operator K-theory
• Verf.angabe: Erik Guentner, Rufus Willett & G. Yu
• Verlagsort: Paris
• Verlag: Société Mathématique de France
• E-Jahr: 2024
• Jahr: [2024]
• Illustrationen: 89 Seiten
• Gesamttitel/Reihe: Astérisque ; 451 (2024)
• Fussnoten: Literaturverzeichnis: Seite [87]-89
• Schrift/Sprache: Zusammenfassungen in englischer und französischer Sprache
• ISBN: 978-2-37905-202-6
• Schlagwörter: (s)Topologische Dynamik / (s)KK-Theorie / (s)Baum-Connes-Vermutung / (s)Gruppoid
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Online-Ausgabe: Guentner, Erik: Dynamical complexity and controlled operator K-Theory. - Paris : Société Mathématique de France, 2024
• RVK-Notation: SI 832
• Sach-SW: K-théorie
• Sach-SW: Topologie algébrique
• Sach-SW: Conjecture de Baum-Connes
• K10plus-PPN: 1903095271

Abstract

Publisher’s description: In this paper, 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.