Authors: David Blanc and George Peschke
Title: The plus construction, Postnikov towers and universal central
module extensions.
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 \ $AX\to X\to X^+$, \ we explain the contribution of
\ $\pi_nX$ \ to \ $\pi_nX^+$, \ $\pi_{n+1}X^+$ \ and \ $\pi_nAX$, \
$\pi_{n+1}AX$ \ explicitly in terms of the low dimensional homology of
$\pi_nX$ regarded as a module over $\pi_1X$. \ Key ingredients developed
here for this purpose are universal $\Pi$-central fibrations and a
theory of universal central extensions of modules, analogous to
universal central extensions of perfect groups.