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Catégorie de Lusternik-Schnirelmann et genre des $H_0$-espaces


Author: M. Cristina Costoya-Ramos
Journal: Proc. Amer. Math. Soc. 131 (2003), 637-645
MSC (2000): Primary 55M30, 55P60, 55P62
DOI: https://doi.org/10.1090/S0002-9939-02-06533-4
Published electronically: June 3, 2002
MathSciNet review: 1933357
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Abstract: Soit $X$ un espace ayant le type d'homotopie rationnelle d'un produit de sphères impaires. Si, pour tout nombre premier $p$, la LS-catégorie de tous les $p$-localisés de $X$ est majorée par $n$, nous montrons que la LS-catégorie de $X$ est majorée par $n+1$. Si $Y$ est un élément dans le genre de Mislin de $X$, nous en déduisons: $\vert{\operatorname{cat}} (Y) - {\operatorname{cat}}(X) \vert\leq 1$. Dans le cas d'un $H$-espace $X$ de rang 2, nous avons exactement ${\operatorname{cat}} (X) = {\operatorname{cat}}(Y)$, pour tout espace $Y$ dans le genre de $X$.


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Additional Information

M. Cristina Costoya-Ramos
Affiliation: U.F.R. de Mathématiques, U.M.R. 8524, Université de Lille 1, 59655 Villeneuve d’Ascq Cedex, France – and – Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
Email: costoya@gat.univ-lille1.fr, costoya@masg1.epfl.ch

DOI: https://doi.org/10.1090/S0002-9939-02-06533-4
Keywords: Lusternik-Schnirelmann category, Mislin genus, $H$-space
Received by editor(s): June 11, 2001
Received by editor(s) in revised form: September 11, 2001
Published electronically: June 3, 2002
Communicated by: Paul Goerss
Article copyright: © Copyright 2002 American Mathematical Society

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