Moore space (algebraic topology)


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 group.

Formal definition

Given an abelian group G and an integer n ≥ 1, let X be a CW complex such that
and
for i ≠ n, 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. Also, X is by definition simply-connected if n>1.

Examples