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Relation Between Higher Obstructions and Postnikov Invariants

Published online by Cambridge University Press:  22 January 2016

Kenichi Shiraiwa
Kenichi Shiraiwa*
Affiliation:
Mathematical Institute, Nagoya University
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The problem of extending a continuous map is one of the most important problems in algebraic topology. Many topologists have contributed for the solution of this problem. One of the most powerful methods in the extension problem is the obstruction theory defined first by S. Eilenberg [1] and developed by many others. N. E. Steenrod worked on the primary obstruction and showed that there is a strong connection between obstruction theory and cohomology operations [7].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 16 , February 1960 , pp. 21 - 33
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1960

References

[1] Eilenberg, S., Cohomology and continuous mappings, Ann. of Math., 41 (1940), 231–251.Google Scholar
[2] Moore, J. C., Semi-simplicial complexes and Postnikov systems, mimeographed note, Princeton University, (1957).Google Scholar
[3] Olum, P., Obstructions to extensions and homotopies, Ann. of Math., 52 (1950), 1–50.CrossRefGoogle Scholar
[4] Peterson, F. P., Functional cohomology operations, Trans. Amer. Math. Soc., 86 (1957), 197–211.Google Scholar
[5] Postnikov, M. M., Investigations in homotopy theory of continuous mappings, Trudy Mat. Inst. Steklov, no. 46. Izdat. Akad. Nauk SSSR, Moscow, 1955 (in Russian).Google Scholar
[6] Shimada, N., Homotopy classification of mappings of a 4-dimensional complex into a 2-dimensional sphere, Nagoya Math. Jour., 5 (1953), 127–144.CrossRefGoogle Scholar
[7] Steenrod, N. E., Products of cocycles and extensions of mappings, Ann. of Math., 48 (1947), 290–320.CrossRefGoogle Scholar
[8] Whitehead, J. H. C., On the theory of obstructions, Ann. of Math., 54 (1951), 68–84.Google Scholar