Homotopy theory of classifying spaces

Abstract: Our research interest has been the homotopy theory of classifying spaces. In the compact case, we described the BZ/p-nullifications of classifying spaces of compact Lie groups (joint with N. Castellana). Moreover, in joint work with R. Foote and J. Scherer, we completely characterized the BZ/p-cellular approximations of classifying spaces, in a program that also implied the classification of all strongly closed subgroups of finite groups. With the second author I also proved an idempotence conjecture of E: Farjoun, and joint with the latter and W. Chachólski we described the cellularizations of nilpotent Postnikov pieces with regard to any base space. BZ/p-cellular approximations of p-local compact groups were also described in joint work with N. Castellana and A. Gavira- Romero.
In the infinite case, we should remark joint work with S. Pooya and A. Valette concerning the Baum-Connes conjecture, which we explicitly established for the case of lamplighter groups; the computation of the minimal dimension of the classifying space for the family of virtually cyclic subgroups of braid groups (joint with J. González-Meneses), and the study of approximations of torsion groups and its relation with the second homotopy group and the classifying space, undertaken in collaboration with F. Muro.