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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...

Balanced splittings of Semi-free actions of finite groups on homotopy spheres.

Douglas R. Anderson, I. Hambleton (1980)

Commentarii mathematici Helvetici

Betti numbers of regions of attraction

Otomar Hájek (1964)

Commentationes Mathematicae Universitatis Carolinae

Bitwisted Burnside-Frobenius theorem and Dehn conjugacy problem

Alexander Fel'shtyn (2009)

Banach Center Publications

It is proved for Abelian groups that the Reidemeister coincidence number of two endomorphisms ϕ and ψ is equal to the number of coincidence points of ϕ̂ and ψ̂ on the unitary dual, if the Reidemeister number is finite. An affirmative answer to the bitwisted Dehn conjugacy problem for almost polycyclic groups is obtained. Finally, we explain why the Reidemeister numbers are always infinite for injective endomorphisms of Baumslag-Solitar groups.

Borsuk-Sieklucki theorem in cohomological dimension theory

Margareta Boege, Jerzy Dydak, Rolando Jiménez, Akira Koyama, Evgeny V. Shchepin (2002)

Fundamenta Mathematicae

The Borsuk-Sieklucki theorem says that for every uncountable family ${X_{α}}_{α \in A}$ of n-dimensional closed subsets of an n-dimensional ANR-compactum, there exist α ≠ β such that $d i m (X_{α} \cap X_{β}) = n$ . In this paper we show a cohomological version of that theorem: Theorem. Suppose a compactum X is $c l c_{ℤ}^{n + 1}$ , where n ≥ 1, and G is an Abelian group. Let ${X_{α}}_{α \in J}$ be an uncountable family of closed subsets of X. If $d i m_{G} X = d i m_{G} X_{α} = n$ for all α ∈ J, then $d i m_{G} (X_{α} \cap X_{β}) = n$ for some α ≠ β. For G being a countable principal ideal domain the above result was proved by Choi and Kozlowski...

Borsuk-Ulam Sätze und Abbildungen mit kompakten Iterierten [Book]

H. Steinlein (1980)

Bourgin–Yang-type theorem for $a$ -compact perturbations of closed operators. I: The case of index theories with dimension property.

Antonyan, Sergey A., Balanov, Zalman I., Gel'man, Boris D. (2006)

Abstract and Applied Analysis

Brouwer degree, equivariant maps and tensor powers.

Balanov, Z., Krawcewicz, W., Kushkuley, A. (1998)

Abstract and Applied Analysis

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...