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Proceedings of the American Mathematical Society

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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.

References [Enhancements On Off] (What's this?)

  • [1] J. F. Adams, The sphere, considered as an H-space $ \bmod\;p$, Quart J. Math. Oxford Ser. (2) 12 (1961), 52-60. MR 23 #A651. MR 0123323 (23:A651)
  • [2] R. D. Porter, An H-space with finite dimensional homology whose loop space has torsion, Proc. Amer. Math. Soc. 37 (1973), 291-292. MR 46 #9970. MR 0310872 (46:9970)
  • [3] J. D. Stasheff, On extensions of H-spaces, Trans. Amer. Math. Soc. 105 (1962), 126-135. MR 31 #2726. MR 0178469 (31:2726)
  • [4] S. Weingram, On the incompressibility of certain maps, Ann. of Math. (2) 93 (1971), 476-485. MR 46 #890. MR 0301735 (46:890)

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Keywords: H-space $ \bmod\;p$
Article copyright: © Copyright 1976 American Mathematical Society

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