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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Extensions of maps as fibrations and cofibrations

Author: Frank Quinn
Journal: Trans. Amer. Math. Soc. 211 (1975), 203-208
MSC: Primary 55D05
MathSciNet review: 0385847
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Abstract: Suppose $ f:X \to Y$ is a map of 1-connected spaces. In the ``stable'' range, roughly where the connectivity of Y exceeds the homology, or homotopy, dimension of X, it is well known that f can be extended as a cofibration $ C \to X \to Y$, or respectively a fibration $ X \to Y \to B$. A criterion is given for the existence of such extensions in a less restrictive ``metastable'' range. A main result is that if f is at least 2-connected and 2 con $ Y \geq \dim Y - 1,\dim X$, then f extends as a cofibration if and only if the map $ (1 \times f)\Delta :X \to (X \times Y)/X$ factors through f.

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Keywords: Fibration, cofibration, metastable extension
Article copyright: © Copyright 1975 American Mathematical Society