2022
DOI: 10.48550/arxiv.2204.13313
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The equivariant coarse Baum-Connes conjecture for actions by a-T-menable groups

Abstract: The equivariant coarse Baum-Connes conjecture was firstly introduced by Roe [29] 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 Γ acts properly and isometrically on a bounded geometry metric space X with controlled distortion such that the quotient space X/Γ is coarsely embeddable, then the equivariant coarse Baum-Connes conjecture holds for this action. This answers a question posed in [8] affirmatively.

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