Cellular properties of nilpotent spaces
نویسندگان
چکیده
We show that cellular approximations of nilpotent Postnikov stages are always nilpotent Postnikov stages, in particular classifying spaces of nilpotent groups are turned into classifying spaces of nilpotent groups. We use a modified Bousfield–Kan homology completion tower zkX whose terms we prove are all X–cellular for any X . As straightforward consequences, we show that if X is K–acyclic and nilpotent for a given homology theory K , then so are all its Postnikov sections PnX , and that any nilpotent space for which the space of pointed self-maps map .X;X / is “canonically” discrete must be aspherical.
منابع مشابه
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