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.
On the Baum-Connes Conjecture for Groups Acting on CAT(0)-Cubical Spaces
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abstract
We give a new proof of the Baum--Connes conjecture with coefficients for any second countable, locally compact topological group that acts properly and cocompactly on a finite-dimensional CAT(0)-cubical space with bounded geometry. The proof uses the Julg-Valette complex of a CAT(0)-cubical space introduced by the first three authors, and the direct splitting method in Kasparov theory developed by the last author.
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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.