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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Equivariant cofibrations and nilpotency


Author: Robert H. Lewis
Journal: Trans. Amer. Math. Soc. 267 (1981), 139-155
MSC: Primary 55P05; Secondary 55P99
MathSciNet review: 621979
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Abstract: Let $ f:B \to Y$ be a cofibration whose cofiber is a Moore space. We give necessary and sufficient conditions for $ f$ to be induced by a map of the desuspension of the cofiber into $ B$. These conditions are especially simple if $ B$ and $ Y$ are nilpotent.

We obtain some results on the existence of equivariant Moore spaces, and use them to construct examples of noninduced cofibrations between nilpotent spaces. Our machinery also leads to a cell structure proof of the characterization of pre-nilpotent spaces due to Dror and Dwyer [7], and to a simple proof, for finite fundamental group, of the result of Brown and Kahn [4] that homotopy dimension equals simple cohomological dimension in nilpotent spaces.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0621979-1
PII: S 0002-9947(1981)0621979-1
Keywords: Nilpotent space, equivariant cofibration, Moore space, pre-nilpotent module, perfect module
Article copyright: © Copyright 1981 American Mathematical Society