Moore space (algebraic topology)
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- See also Moore space for other meanings in mathematics.
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.
[edit] 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 Hn(X) 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.
[edit] Examples
- Sn is a Moore space of
for 
.
is a Moore space of 
(n=1).
[edit] References
- Hatcher, Allen. Algebraic topology, Cambridge University Press (2002), ISBN 0-521-79540-0. For further discussion of Moore spaces, see Chapter 2, Example 2.40. A free electronic version of this book is available on the author's homepage.
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