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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The diagonal fibration, $ H$-spaces, and duality


Author: David Handel
Journal: Proc. Amer. Math. Soc. 36 (1972), 275-279
MSC: Primary 55D45
DOI: https://doi.org/10.1090/S0002-9939-1972-0307228-2
MathSciNet review: 0307228
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Abstract: For any pointed topological space X, there is the fibration $ \Omega X \to {X^I} \to X \times X$ whose projection sends the map $ f:I \to X$ to $ (f(0),f(1))$. We show that if X has the based homotopy type of a CW complex, then the above fibration is equivalent to one induced from the path space fibration $ \Omega X \to PX \to X$ if and only if X admits an H-space multiplication. Dually, we obtain a characterization of simply-connected co-H-spaces.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0307228-2
Keywords: Induced fibration, induced cofibration, H-space, co-H-space, diagonal map, codiagonal map
Article copyright: © Copyright 1972 American Mathematical Society