Moore space of a group

Definition
Given an Abelian group $$G$$ and an integer $$n \ge 1$$, the Moore space $$M(G,n)$$ is a topological space $$X$$ such that:


 * $$H_n(X) = G$$
 * $$\tilde{H}_i(X) = 0$$ for $$i \ne n$$
 * If $$n > 1$$, then $$X$$ is simply connected

The Moore space is explicitly constructed as a CW-space by first using $$n$$-cells and $$(n+1)$$-cells.

Related notions

 * Eilenberg-Maclane space