Compressible maps
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- by Jay E. Goldfeather
- Proc. Amer. Math. Soc. 60 (1976), 339-342
- DOI: https://doi.org/10.1090/S0002-9939-1976-0423339-9
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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
- J. F. Adams, The sphere, considered as an $H$-space $\textrm {mod}\,p$, Quart. J. Math. Oxford Ser. (2) 12 (1961), 52–60. MR 123323, DOI 10.1093/qmath/12.1.52
- Richard D. Porter, An $H$-space with finite dimensional homology whose loop space has torsion, Proc. Amer. Math. Soc. 37 (1973), 291–292. MR 310872, DOI 10.1090/S0002-9939-1973-0310872-0
- James Dillon Stasheff, On extensions of $H$-spaces, Trans. Amer. Math. Soc. 105 (1962), 126–135. MR 178469, DOI 10.1090/S0002-9947-1962-0178469-0
- Stephen Weingram, On the incompressibility of certain maps, Ann. of Math. (2) 93 (1971), 476–485. MR 301735, DOI 10.2307/1970885
Bibliographic 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