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The group of homotopy self-equivalences of non-simply-connected spaces using Postnikov decompositions II1

Published online by Cambridge University Press:  14 November 2011

John W. Rutter
John W. Rutter
Affiliation:
Institut des Haut Études Scientifique, 91440 Bures sur Yvette, France; and Department of Pure Mathematics, Liverpool University Liverpool L69 3BX, UK.
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Synopsis

We give here an abelian kernel (central) group extension sequence for calculating, for a non-simply-connected space X, the group of pointed self-homotopy-equivalence classes . This group extension sequence gives in terms of , where Xn is the nth stage of a Postnikov decomposition, and, in particular, determines up to extension for non-simplyconnected spaces X having at most two non-trivial homotopy groups in dimensions 1 and n. We give a simple geometric proof that the sequence splits in the case where is the generalised Eilenberg–McLane space corresponding to the action ϕ: π1 → aut πn, and give some information about the class of the extension in the general case.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 122 , Issue 1-2 , 1992 , pp. 127 - 135
Copyright
Copyright © Royal Society of Edinburgh 1992

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References

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