Girish Mahajan (Editor)

Moore space (algebraic topology)

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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.

Contents

Formal definition

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

H n ( X ) ≅ G

and

H ~ i ( X ) ≅ 0

for i ≠ n, where H n ( X ) denotes the n-th singular homology group of X and H ~ i ( X ) is the ith reduced homology group. Then X is said to be a Moore space.

Examples

  • S n is a Moore space of Z for n ≥ 1 .
  • R P 2 is a Moore space of Z / 2 Z (n=1).

    • References

    Moore space (algebraic topology) Wikipedia
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