# nLab Moore space

The Moore space $M\left(G,n\right)$, where $G$ is an abelian group and $n\ge 1$, is a space which has non-trivial (reduced) homology group $G$ only in dimension $n$. There is also a cohomology analogue known as a co-Moore space, but this is not defined for all abelian $G$. Spheres are both Moore and co-Moore spaces for $G=ℤ$.

Co-Moore spaces are the Eckmann–Hilton duals of Eilenberg–Mac Lane spaces.

According to Baues, Moore spaces are $H\pi$-duals to Eilenberg–Mac Lane spaces. This leads to an extensive duality for connected CW complexes.

Just as there is a Postnikov decomposition of a space as a tower of fibrations, so there is a Moore decomposition? as a tower of cofibrations.

## References

Revised on June 18, 2013 10:48:14 by Tim Porter (95.147.236.136)