Abstract
Given a connected spaceX, we consider the effect of Quillen’s plus construction on the homotopy groups ofX in terms of its Postnikov decomposition. Specifically, using universal properties of the fibration sequenceAX→X→X +, we explain the contribution of π n X to π n X +, π n+1 X + and π n AX, π n+1 AX explicitly in terms of the low dimensional homology of π n X regarded as a module over π1 X. 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.
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Research partially supported by NSERC of Canada.
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Blanc, D., Peschke, G. The plus construction, Postnikov towers and universal central module extensions. Isr. J. Math. 132, 109–123 (2002). https://doi.org/10.1007/BF02784507
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DOI: https://doi.org/10.1007/BF02784507