For groups with a gamma element, Spanier-Whitehead K-duality holds exactly when the strong Baum-Connes conjecture holds, and all a-T-menable groups with a G-compact model of EG satisfy this duality.
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Groups with Spanier-Whitehead duality
For groups with a gamma element, Spanier-Whitehead K-duality holds exactly when the strong Baum-Connes conjecture holds, and all a-T-menable groups with a G-compact model of EG satisfy this duality.