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Dynamical complexity and $K$ -theory of $L^{p}$ operator crossed products

Institute of Mathematics of the Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warszawa, Poland

https://doi.org/10.1142/S1793525320500314Cited by:3 (Source: Crossref)

Abstract

We apply quantitative (or controlled) $K$ -theory to prove that a certain $L^{p}$ assembly map is an isomorphism for $p \in [1, \infty)$ when an action of a countable discrete group $Γ$ on a compact Hausdorff space $X$ has finite dynamical complexity. When $p = 2$ , this is a model for the Baum–Connes assembly map for $Γ$ with coefficients in $C (X)$ , and was shown to be an isomorphism by Guentner et al.

Keywords:

AMSC: 19K56, 46L80, 46L85, 47L10, 37B05

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