Grups i espais classificadors

We intend to pursue the study of the cohomology of classifying spaces and their homotopy uniqueness, analyzing also the localization techniques that are systematically used in this context. Starting from several recent results by Jackowsky-McClure-Oliver, Dwyer-Miller-Wilkerson and Lannes, some still unpublished, we shall study specific constructions of finite loop spaces and their homotopy properties. The application of localization theory to the study of the cohomology of non-nilpotent groups and spaces requires more abstract and careful methods than in the classical case. Our approach is based on the connection found between the homology of a discrete group and the possibility of extracting roots in it, as well as on the idea of taking into account the actions of operators on the higher homotopy groups of spaces. We shall study the localization of arbitrary fibrations of connected spa