2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62618Suppose X is any finite complex with vanishing L^2 Betti number. We prove upper bounds on the Betti numbers for regular coverings of X, sublinear in the order of covering. The bounds are sensitive to the Novikov-Shubin invariants of X, and are improved in the presence of a spectral gap.22 pagesGeometric TopologyDifferential Geometry57M10text