Compressible Maps

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.