Equivariant cofibrations and nilpotency

Abstract

Let f : B → Y f:B \to Y be a cofibration whose cofiber is a Moore space. We give necessary and sufficient conditions for f f to be induced by a map of the desuspension of the cofiber into B B . These conditions are especially simple if B B and Y 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.