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- Comparing seminorms on homology doi link

Auteur(s): Lafont Jean-François, Pittet Christophe

(Article) Publié: Pacific Journal Of Mathematics (Project Euclid), vol. 259 p.373--385 (2012)


Ref HAL: hal-01305010_v1
DOI: 10.2140/pjm.2012.259.373
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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.