Jump to content

Moore space (algebraic topology)

From Wikipedia, the free encyclopedia

This is an old revision of this page, as edited by CBM (talk | contribs) at 13:01, 20 June 2017 (Manually reviewed edit to replace magic words per local rfc). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

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

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

and

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.

Examples

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

See also

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.