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A Remark on (π, n)-Type CW-Complexes

Published online by Cambridge University Press:  22 January 2016

Kenichi Shiraiwa
Kenichi Shiraiwa*
Affiliation:
Mathematical Institute, Nagoya University
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Let X be a space whose i-th homotopy group πi(X)vanishes for every i ≧ 0 except i = n ≧ 1, and whose n-th homotopy group is isomorphic to a group π. Then it is well known that the polyhedral homotopy type of X is completely determined by π and n. We call such a space a (π, n)-type space. Also it is well known that the minimal complex of the singular complex of a (π, n)-type space is isomorphic to the complex K(π, n)defined by S. Eilenberg and S. MacLane [1]. We know also that for any n ≧ 1 and any group π(abelian if n > 1) there exists a (π, n)-type space (See [6]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 12 , December 1957 , pp. 25 - 30
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1957

References

[1] Eilenberg, S. and MacLane, S.: Relations between homotopy and homology groups of spaces I, II, Ann. of Math., 46 (1945), pp. 480–509; 51 (1950), pp. 514–533.Google Scholar
[2] Cartan, H.: Séminaire de topologie algébrique, 1954/55.Google Scholar
[3] Serre, J. P.: Groupes d’homotopie et classes de groupes abéliens, Ann. of Math., 58 (1953), pp. 258–294.Google Scholar
[4] Toda, H.: Generalized Whitehead products and homotopy groups of spheres, J. Inst. Polyt. Osaka City Univ., 3 (1952), pp. 43–82.Google Scholar
[5] Whitehead, J. H. C.: On simply connected 4-dimensional polyhedra, Comm. Math. Helv., 22 (1949), pp. 48–92.Google Scholar
[6] Whitehead, J. H. C.: On the readability of homotopy groups, Ann. of Math., 50 (1949), pp. 261–263.CrossRefGoogle Scholar
[7] Whitehead, J. H. C.: On the homotopy type of ANR’s, Bull. Amer. Math. Soc, 54 (1948), pp. 1133–1145.Google Scholar