The equivariant coarse Baum–Connes conjecture for actions by a-T-menable groups
Volume 275 / 2024
Studia Mathematica 275 (2024), 99-146
MSC: Primary 46L80; Secondary 46H35, 58B34
DOI: 10.4064/sm230417-7-2
Published online: 21 May 2024
Abstract
The equivariant coarse Baum–Connes conjecture was first introduced by Roe in 1996 as a unified way to approach both the Baum–Connes conjecture and its coarse counterpart. In this paper, we prove that if an a-T-menable group $\Gamma $ acts properly and isometrically on a bounded geometry metric space $X$ with controlled distortion such that the quotient space $X/\Gamma $ is coarsely embeddable, then the equivariant coarse Baum–Connes conjecture holds for this action. This answers affirmatively a question posed by Deng, Fu and Wang in 2024.
