$L^p$ coarse Baum–Connes conjecture and $K$-theory for $L^p$ Roe algebras

Jianguo Zhang; Dapeng Zhou

doi:10.4171/jncg/435

JournalsjncgVol. 15, No. 4pp. 1285–1322

$L^{p}$ coarse Baum–Connes conjecture and $K$ -theory for $L^{p}$ Roe algebras

Jianguo Zhang
Fudan University, Shanghai, China
Dapeng Zhou
East China Normal University, Shanghai, China

Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

In this paper, we verify the $L^{p}$ coarse Baum–Connes conjecture for spaces with finite asymptotic dimension for $p \in [1, \infty)$ . We also show that the $K$ -theory of $L^{p}$ Roe algebras is independent of $p \in (1, \infty)$ for spaces with finite asymptotic dimension.

Cite this article

Jianguo Zhang, Dapeng Zhou, $L^{p}$ coarse Baum–Connes conjecture and $K$ -theory for $L^{p}$ Roe algebras. J. Noncommut. Geom. 15 (2021), no. 4, pp. 1285–1322

DOI 10.4171/JNCG/435