In this paper we find a formula for the rational LS-category of certain elliptic spaces which generalizes or complements previous work of the subject. This formula is given in terms of the minimal model of the space.
Let p be a prime number and X a simply connected Hausdorff space equipped with a free -action generated by . Let be a homeomorphism generating a free -action on the (2n-1)-sphere, whose orbit space is some lens space. We prove that, under some homotopy conditions on X, there exists an equivariant map . As applications, we derive new versions of generalized Lusternik-Schnirelmann and Borsuk-Ulam theorems.
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...
In this paper we introduce the categorical length, a homotopy version of Fox categorical sequence, and an extended version of relative L-S category which contains the classical notions of Berstein-Ganea and Fadell-Husseini. We then show that, for a space or a pair, the categorical length for categorical sequences is precisely the L-S category or the relative L-S category in the sense of Fadell-Husseini respectively. Higher Hopf invariants, cup length, module weights, and recent computations by Kono...
Our point of departure is J. Neisendorfer's localization theorem which reveals a subtle connection between some simply connected finite complexes and their connected covers. We show that even though the connected covers do not forget that they came from a finite complex their homotopy-theoretic properties are drastically different from those of finite complexes. For instance, connected covers of finite complexes may have uncountable genus or nontrivial SNT sets, their Lusternik-Schnirelmann category...