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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A relation between obstructions and functional cohomology operations


Author: Robert D. Little
Journal: Proc. Amer. Math. Soc. 49 (1975), 475-480
MSC: Primary 55G35
MathSciNet review: 0418099
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Abstract: In a recent paper, P. Olum developed a formula which relates the obstruction to an extension and the induced homomorphism in cohomology. In the present paper, we develop an analogous formula which relates the obstruction to an extension and a certain functional cohomology operation. This operation is a generalization of the standard functional cohomology operation of Steenrod. Olum showed that his formula is particularly useful when the range space of the extension problem is one of the classifying spaces BU, BO, or BSp. Our formula is also useful in this context and we show that it can be used to compute the obstruction in certain situations where the Olum formula fails.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0418099-0
PII: S 0002-9939(1975)0418099-0
Keywords: Extension problems, obstructions, functional cohomology operations, Steenrod powers, Postnikov systems, the classifying spaces BU, BO, BSp
Article copyright: © Copyright 1975 American Mathematical Society