Volume of Riemannian manifolds, geometric inequalities, and homotopy theory

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77626We outline the current state of knowledge regarding geometric inequalities of systolic type, and prove new results, including systolic freedom in dimension 4. Namely, every compact, orientable, smooth 4-manifold X admits metrics of arbitrarily small volume such that every orientable, immersed surface of smaller than unit area is necessarily null-homologous in X.25 pages, LaTeX2e, 3 figures. To appear in the Rothenberg Festschrift, Contemporary MathDifferential GeometryAlgebraic Topology53C23 (Primary); 55Q15 (Secondary)Volume of Riemannian manifolds, geometric inequalities, and homotopy theorytext