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Some function spaces of CW type


Author: Peter J. Kahn
Journal: Proc. Amer. Math. Soc. 90 (1984), 599-607
MSC: Primary 55P99; Secondary 54E60
DOI: https://doi.org/10.1090/S0002-9939-1984-0733413-X
MathSciNet review: 733413
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Abstract: J. Milnor's result on the CW type of certain function spaces $ {\operatorname{map}}\left( {X,Y} \right)$ is extended to allow the case in which $ X$ has a finite $ k$-skeleton and $ {\pi _i}Y = 0$, $ i > k$. One conclusion is that the self-equivalence monoid of any Postnikov stage of a finite complex has CW type. Another is that the monoid of pointed self-equivalences of a $ K\left( {\pi ,1} \right)$ manifold has contractible components when $ \pi $ is finitely-generated.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0733413-X
Keywords: Homotopy type, CW complex, function space
Article copyright: © Copyright 1984 American Mathematical Society

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