Moore space of a group

Definition

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

• $H_{n}(X)=G$
• ${\tilde {H}}_{i}(X)=0$ for $i\neq n$
• 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