Moore space (algebraic topology)

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For other uses, see Moore space (disambiguation).

In algebraic topology, a branch of mathematics, Moore space is the name given to a particular type of topological space that is the homology analogue of the Eilenberg–Maclane spaces of homotopy theory, in the sense that it has only one nonzero homology (rather than homotopy) group.

Formal definition[edit]

Given an abelian group G and an integer n ≥ 1, let X be a CW complex such that


for in, where denotes the n-th singular homology group of X and is the ith reduced homology group. Then X is said to be a Moore space.


  • is a Moore space of for .
  • is a Moore space of (n=1).

See also[edit]