The plus construction, Postnikov towers and universal central module extensions |
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Authors: | David Blanc George Peschke |
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Affiliation: | (1) Department of Mathematics, University of Haifa, 31905 Haifa, Israel;(2) Department of Mathematical Sciences, University of Alberta, T6G 2G1 Edmonton, Canada |
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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. Research partially supported by NSERC of Canada. |
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