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Whitney-sums (fibre-joins) in over space theory and obstruction theory for cohomology with local coefficients*

Published online by Cambridge University Press:  14 November 2011

John W. Rutter
John W. Rutter
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Cambridge University, 16, Mill Lane, Cambridge CB2 1SB, U.K.; and Department of Pure Mathematics, Liverpool University, Liverpool L69 3BX, England, U.K.
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Synopsis

The generalised Whitney sum (fibre-join) and the h-fibre-join can be defined in topM, the category of spaces over M. We note here some general properties of these constructions, and, as a specific example, we consider the relation between them and the extensions to the topM category of the top h-fibre-sequences F∗ΩB→E ∪ CF→B determined by top fibrations F→E→B. As an application we obtain the truncated local coefficient cohomology sequence for a top fibration which is topM principal fibration: this situation applies, for example, to the various stages of the Postnikov decomposition of a non-simply connected space X, and in this case we have M = K1(π1(X)).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 115 , Issue 3-4 , 1990 , pp. 359 - 365
Copyright
Copyright © Royal Society of Edinburgh 1990

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References

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