The plus construction, Postnikov towers and universal central module extensions |
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Authors: | David Blanc George Peschke |
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Institution: | (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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Keywords: | |
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