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Killing space

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A fibre space p _ {n} : ( X , n ) \rightarrow X for which the homotopy groups \pi _ {i} ( X , n ) vanish if i < n , and p _ {n*} : \pi _ {i} ( X , n ) \rightarrow \pi _ {i} ( X) is an isomorphism if i \geq n . The space ( X , n ) is constructed by induction with respect to n . If ( X , n - 1 ) has already been constructed, then ( X , n ) is taken to be the homotopy fibre of the canonical mapping

( X , n - 1 ) \rightarrow K ( \pi _ {n-} 1 ( X) , n - 1 ) ,

K ( \pi _ {n-} 1 ( X) , n - 1 ) denoting an Eilenberg–MacLane space. The sequence of spaces ( X , n ) and mappings p _ {n} is a Moore–Postnikov system of the mapping * \rightarrow X .

Comments

See also [a1], Chapt. 8, Sect. 3.

References

[a1] E.H. Spanier, "Algebraic topology" , McGraw-Hill (1966) pp. Chapt. 2
How to Cite This Entry:
Killing space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Killing_space&oldid=47498
This article was adapted from an original article by A.F. Kharshiladze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article