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Classification of Mappings of an (n + 2)-Complex into an (n − 1)-Connected Space with Vanishing (n + 1)-st Homotopy Group

Published online by Cambridge University Press:  22 January 2016

Nobuo Shimada  and
Hiroshi Uehara
Nobuo Shimada
Affiliation:
Mathematical Institute, Nagoya University
Hiroshi Uehara
Affiliation:
Mathematical Institute, Nagoya University
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The present paper is concerned with the classification and corresponding extension theorem of mappings of the (n+-2)-complex Kn+2 (n>2) into the space Y whose homotopy groups πi(Y) vanish for i < n and i = n+1, and the n-th homotopy group πn(Y) of which has a finite number of generators. Our methods followed here are essentially analogous to those of Steenrod [2].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 4 , June 1952 , pp. 43 - 50
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1952

References

[1] Pontrjagin, L., Mappings of the 3-dimensional sphere into an n-dimensional complex, C. R. Acad Sci. URSS., 31 (1942), 35–37.Google Scholar
[2] Steenrod, N. E., Products of cocycles and extensions of mappings, Ann. of Math., 48 (1947), 290–320.Google Scholar
[3] Whitney, H., An extension theorem for mappings into simply connected spaces, Ann. of Math., 50 (1949), 285–296.Google Scholar
[4] Whitehead, J. H. C., On simply connected, 4-dimensional polyhedra, Comm. Math. Helv., 22 (1949), 48–92.Google Scholar
[5] Whitehead, J. H. C., The homotopy type of a special kind of polyhedron, Annals de la Soc. Polon, der Math., 21 (1948), 176–186. (This is inaccessible to us here.)Google Scholar
[6] Whitehead, J. H. C., On adding relations to homotopy groups, Ann of Math., 42 (1941), 409–428.Google Scholar
[7] Eilenberg, S. and MacLane, S., Relations between homology and homotopy groups of spaces II, Ann. of Math., 51 (1950) 514–533.CrossRefGoogle Scholar
[8] Whitehead, G. W., A generalization of the Hopf invariant, Ann. of Math., 51 (1950), 192–237.Google Scholar
[9] Whitehead, G. W., The (n + 2)-nd homotopy group of the n-sphere, Ann. of Math., 52 (1950), 245–247.Google Scholar
[10] Pontrjagin, L., C. R. Acad. Sci. URSS, 70 (1950), 957–959.Google Scholar
[11] Blakers, A. L. and Massay, W. S., Homotopy groups of a triad I, Ann, of Math., 53 (1951), 161–205.Google Scholar
[12] Chang, S. C., Homotopy invariants and continuous mappings, Proc. Roy. Soc. of London, A, 202 (1950), 253–263.Google Scholar
[13] Uehara, H., On homotopy type problems of special kind of polyhedra, to appear shortly.Google Scholar