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Fibrations in the Category of Absolute Neighborhood Retracts

Takahisa Miyata (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

The category Top of topological spaces and continuous maps has the structures of a fibration category and a cofibration category in the sense of Baues, where fibration = Hurewicz fibration, cofibration = the usual cofibration, and weak equivalence = homotopy equivalence. Concentrating on fibrations, we consider the problem: given a full subcategory 𝓒 of Top, is the fibration structure of Top restricted to 𝓒 a fibration category? In this paper we take the special case where 𝓒 is the full subcategory...

Induced mappings of homology decompositions

Martin Arkowitz (1998)

Banach Center Publications

We give conditions for a map of spaces to induce maps of the homology decompositions of the spaces which are compatible with the homology sections and dual Postnikov invariants. Several applications of this result are obtained. We show how the homotopy type of the (n+1)st homology section depends on the homotopy type of the nth homology section and the (n+1)st homology group. We prove that all homology sections of a co-H-space are co-H-spaces, all n-equivalences of the homology decomposition are...

Quelques contre-exemples pour la LS catégorie d'une algèbre de cochaînes

Elhassan Idrissi (1991)

Annales de l'institut Fourier

À toute algèbre de cochaînes A sont associés les invariants numériques suivants : bi M cat ( A ) , r M cat ( A ) et l M cat ( A ) qui approximent, pour tout corps k et lorsque A = C * ( X ; k ) , la catégorie au sens de Lusternik-Schnirelmann de l’espace X . Nous montrons dans cet article que ces trois invariants sont deux à deux distincts.

The Gray filtration on phantom maps

Lê Minh Hà, Jeffrey Strom (2001)

Fundamenta Mathematicae

This paper is a study of the Gray index of phantom maps. We give a new, tower theoretic, definition of the Gray index, which allows us to study the naturality properties of the Gray index in some detail. McGibbon and Roitberg have shown that if f* is surjective on rational cohomology, then the induced map on phantom sets is also surjective. We show that if f* is surjective just in dimension k, then f induces a surjection on a certain subquotient of the phantom set. If the condition...

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