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ON TOWERS APPROXIMATING HOMOLOGICAL LOCALIZATIONS
Published online by Cambridge University Press: 01 December 1997
Abstract
Our object of study is the natural tower which, for any given map f[ratio ]A→B and each space X, starts with the localization of X with respect to f and converges to X itself. These towers can be used to produce approximations to localization with respect to any generalized homology theory E∗, yielding, for example, an analogue of Quillen's plus-construction for E∗. We discuss in detail the case of ordinary homology with coefficients in ℤ/p or ℤ[1/p]. Our main tool is a comparison theorem for nullification functors (that is, localizations with respect to maps of the form f[ratio ]A→pt), which allows us, among other things, to generalize Neisendorfer's observation that p-completion of simply-connected spaces coincides with nullification with respect to a Moore space M(ℤ[1/p], 1).
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- The London Mathematical Society 1997
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