Abstract
Our object of study is the natural tower which, for any given map f: 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: 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).
Original language | English |
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Pages (from-to) | 645-656 |
Journal | Journal of the London Mathematical Society |
Volume | 56 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Jan 1997 |