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A formula for the rational LS-category of certain spaces

Luis Lechuga, Aniceto Murillo (2002)

Annales de l’institut Fourier

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.

A note on the theorems of Lusternik-Schnirelmann and Borsuk-Ulam

T. E. Barros, C. Biasi (2008)

Colloquium Mathematicae

Let p be a prime number and X a simply connected Hausdorff space equipped with a free p -action generated by f p : X X . Let α : S 2 n - 1 S 2 n - 1 be a homeomorphism generating a free p -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 F : ( S 2 n - 1 , α ) ( X , f p ) . As applications, we derive new versions of generalized Lusternik-Schnirelmann and Borsuk-Ulam theorems.

Axiome du cube et foncteurs de Quillen

Jean-Pierre Doeraene, Daniel 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...

Categorical length, relative L-S category and higher Hopf invariants

Norio Iwase (2009)

Banach Center Publications

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...

Connected covers and Neisendorfer's localization theorem

C. McGibbon, J. Møller (1997)

Fundamenta Mathematicae

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...

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