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Proceedings of the American Mathematical Society

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



Compressible maps

Author: Jay E. Goldfeather
Journal: Proc. Amer. Math. Soc. 60 (1976), 339-342
MSC: Primary 55D35
MathSciNet review: 0423339
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Abstract: Weingram has shown that if G is a finitely generated abelian group, then every nontrivial map $f:\Omega {S^{2n + 1}} \to K(G,2n)$ is incompressible; that is, f is not homotopic to a map whose image is contained in some finite-dimensional skeleton. It is shown that a nontrivial map $\Omega {S^{2n + 1}} \to K(G,2n)$ may be compressible if G is not finitely generated. This result leads to some understanding of the obstructions to compressibility in Weingram’s Theorem.

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Keywords: <I>H</I>-space <IMG WIDTH="62" HEIGHT="39" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$\bmod \;p$">
Article copyright: © Copyright 1976 American Mathematical Society