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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Compressible maps
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by Jay E. Goldfeather PDF
Proc. Amer. Math. Soc. 60 (1976), 339-342 Request permission

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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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 339-342
  • MSC: Primary 55D35
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0423339-9
  • MathSciNet review: 0423339