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LS-catégorie de CW-complexes à 3 cellules en théorie homototique R-locale.

Hans ScheererDaniel Tanré — 1997

Publicacions Matemàtiques

We study the Lusternik-Schnirelmann category of some CW-complexes with 3 cells, built on Y = S U e. In particular, we prove that an R-local space, in the sense of D. Anick, of LS-category 3 and of the homotopy type of a CW-complex with 3 R-cells, has a cup-product of length 3 in its algebra of cohomology. This result is no longer true in the framework of mild spaces.

Exploring W.G. Dwyer's tame homotopy theory.

Hans ScheererDaniel Tanré — 1991

Publicacions Matemàtiques

Let S be the category of r-reduced simplicial sets, r ≥ 3; let L be the category of (r-1)-reduced differential graded Lie algebras over Z. According to the fundamental work [3] of W.G. Dwyer both categories are endowed with closed model category structures such that the associated tame homotopy category of S is equivalent to the associated homotopy category of L. Here we embark on a study of this equivalence and its implications. In particular, we show how to compute homology, cohomology, homotopy...

Axiome du cube et foncteurs de Quillen

Jean-Pierre DoeraeneDaniel Tanré — 1995

Annales de l'institut Fourier

Les approches de Whitehead et de Ganea, conceptuellement différentes, permettent toutes deux la définition de la catégorie de Lusternik et Schnirelmann. Le premier auteur a montré qu’elles existent dans le cadre des catégories à modèles de Quillen et qu’elles coïncident lorsqu’est vérifié un axiome supplémentaire non autodual, l’axiome du cube. Nous étendons ici cette étude au cadre de catégories à modèles non nécessairement propres et ne vérifiant pas l’axiome du cube. Pour cela, l’hypothèse globale...

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