Geometric property (T) for non-discrete spaces

Geometric property (T) was defined by Willett and Yu, first for sequences of graphs later more general discrete spaces. Increasing with geometric are expanders, they examples coarse spaces which the maximal Baum-Connes assembly map fails to be surjective. Here, we give a broader definition bounded geometry spaces, includes non-discrete We define generalisation this class show that it is invariant. Additionally, characterise in terms spectral properties Laplacians. investigate manifolds warped systems.