  We explain the coarse geometric origin of the fact that certain spectral
subspaces of topological insulator Hamiltonians are delocalized, in the sense
that they cannot admit an orthonormal basis of localized wavefunctions, with
respect to any uniformly discrete set of localization centers. This is a robust
result requiring neither spatial homogeneity nor symmetries, and applies to
Landau levels of disordered quantum Hall systems on general Riemannian
manifolds.
