Adams completion for CW-Complexes

Abstract

The acyclic tower can be obtained through a general categorical completion process due to Adams. More precisely, the different stages of the acyclic tower of a space are obtained as the Adams completion of the space with respect to the carefully chosen sets of morphisms; it is done in the context of a Serre class of abelian groups. Postnikov-like approximation is obtained for a 1-connected based nilpotent space, in terms of Adams completion with respect to a suitable sets of morphisms, using the primary homotopy theory developed by Neisendonfer. Also Cartan-Whitehead decomposition is obtained for a 0-connected based nilpotent space, in terms of Adams cocompletion with respect to properly chosen sets of morphisms, using the primary homotopy theory developed by Neisendonfer. Under suitable assumption it is proved that weak fibration implies fibration and weak cofibration implies cofibration, as introduced by Bauer and Dugundji.