2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158914We show that for closed orientable manifolds the $k$-dimensional stable systole admits a metric-independent volume bound if and only if there are cohomology classes of degree $k$ that generate cohomology in top-degree. Moreover, it turns out that in the nonorientable case such a bound does not exist for stable systoles of dimension at least two. Additionally, we prove that the stable systolic constant depends only on the image of the fundamental class in a suitable Eilenberg-Mac Lane space. Consequently, the stable $k$-systolic constant is completely determined by the multilinear intersection form on $k$-dimensional cohomology.15 pages; Theorem 1.4 is improved, the dependence on the intersection form is clearifiedGeometric TopologyDifferential Geometry53C23, 53C20text