Abstract
AbstractGiven an ample groupoid, we construct a spectral sequence with groupoid homology with integer coefficients on the second sheet, converging to theK-groups of the (reduced) groupoid C$^*$-algebra, provided the groupoid has torsion-free stabilizers and satisfies a strong form of the Baum–Connes conjecture. The construction is based on the triangulated category approach to the Baum–Connes conjecture developed by Meyer and Nest. We also present a few applications to topological dynamics and discuss the HK conjecture of Matui.
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