Equivariant cofibrations and nilpotency

Lewis, Robert H.

doi:10.1090/S0002-9947-1981-0621979-1

Equivariant cofibrations and nilpotency
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Trans. Amer. Math. Soc. 267 (1981), 139-155 Request permission

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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