2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101219We show that, for any $k\geq 1$, there exist non-formal compact orientable $(k-1)$-connected $n$-manifolds with $k$-th Betti number $b_k=b\geq 0$ if and only if $n\geq \max \{4k-1, 4k+3-2b\}$.12 pages, no figures, latex2e, minor correctionsAlgebraic TopologyDifferential Geometry55S30; 55P62text