Given a connected space X, we consider the effect of Quillen's plus construction on the homotopy groups of X in terms of its Postnikov decomposition. Specifically, using universal properties of the fibration sequence AX → X → X+, we explain the contribution of πnX to πn X+, πn+1 X+ and πnAX, πn+1 AX explicitly in terms of the low dimensional homology of πnX regarded as a module over π1X. Key ingredients developed here for this purpose are universal II-central fibrations and a theory of universal central extensions of modules, analogous to universal central extensions of perfect groups.
ASJC Scopus subject areas
- Mathematics (all)