A UNIVERSAL SPACE FOR PLUS-CONSTRUCTIONS

A.J. BERRICK, CARLES CASACUBERTA
1999 Topology  
We exhibit a two-dimensional, acyclic, Eilenberg-Mac Lane space ¼ such that, for every space X, the plusconstruction X> with respect to the largest perfect subgroup of (X) coincides, up to homotopy, with the ¼-nullification of X; that is, the natural map XPX> is homotopy initial among maps XP½ where the based mapping space map * (¼, ½ ) is weakly contractible. Furthermore, we describe the effect of ¼-nullification for any acyclic ¼, and show that some of its properties imply, in their turn, the acyclicity of ¼.
doi:10.1016/s0040-9383(97)00073-6 fatcat:xans2eggmvfjzedblovem6ajcq