%0 Journal Article
%T Comparing seminorms on homology
%+ Mathematics Department, The Ohio State University
%+ Laboratoire d'Analyse, Topologie, Probabilités (LATP)
%A Lafont, Jean-François
%A Pittet, Christophe
%< avec comité de lecture
%@ 0030-8730
%J Pacific Journal of Mathematics
%I Mathematical Sciences Publishers
%V 259
%N 2
%P 373--385
%8 2012
%D 2012
%R 10.2140/pjm.2012.259.373
%K /1-norm
%K simplicial volume
%K singular homology
%K manifold norm
%K Steenrod’s realization problem
%K Thurston norm
%K Tomei manifold
%Z 53C23; 57M50
%Z Mathematics [math]/Differential Geometry [math.DG]Journal articles
%X 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.
%G English
%L hal-01305010
%U https://hal.science/hal-01305010
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ INSMI