Comparing seminorms on homology
Résumé
We compare the l1-seminorm ̇1 and the manifold seminorm ̇man on n-dimensional integral homology classes. Crowley and Löh showed that for any topological space X and any α ε Hn.(X;Z) with n ≠ 3, the equality αman =α1 holds. We compute the simplicial volume of the 3-dimensional Tomei manifold and apply Gaifullin's desingularization to establish the existence of a constant δ3≈0.0115416, with the property that for any X and any α εH3(XI Z) one has the inequality.