Rectified Baum-Connes conjecture for transformation groupoids
Rectified Baum-Connes conjecture for transformation groupoids
Let be a finitely generated discrete group acting on a metrizable finite-dimensional compact space , and let . Write for the domain of the Baum-Connes map, let be the maximal crossed-product completion, and let be the Baum-Guentner-Willett minimal exact and Morita-compatible crossed product. For , let
be the composite of the maximal Baum-Connes map with the natural map from to . Rectified Baum-Connes conjecture. The morphism is an isomorphism for every . The conjecture is presented as the rectified replacement for the reduced Baum-Connes conjecture, whose groupoid version has counterexamples; the source states that Baum, Guentner and Willett established the relevant minimal crossed-product framework, but does not state that this conjecture is resolved in the generality above.
Sources & referencesView supporting material
Primary source
Moulay-Tahar Benameur and Victor Moulard, “Admissible Higson-Roe sequences for transformation groupoids”, arXiv:2411.00182 (2025).
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