Admissible Higson-Roe sequences for transformation groupoids
Given a finitely generated discrete group Γ, we construct for any admissible crossed product completion and for any metrizable finite dimensional compact Γ-space X, a universal Higson-Roe six-term exact sequence for the transformation groupoid X\rtimes Γ. In particular, we generalize the maximal Higson- Roe sequence to such groupoids. In the case where the groupoid X\rtimes Γ satisfies the rectified Baum-Connes conjecture, this yields some rigidity consequences.
math.OA↗