On Towers Approximating Homological Localizations |
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Authors: | Casacuberta Carles; Rodriguez Jose L |
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Institution: | Departament de Matemàtiques, Universitat Autònoma de Barcelona E-08193 Bellaterra, Spain. E-mail: casac{at}mat.uab.es
Departament de Matemàtiques, Universitat Autònoma de Barcelona E-08193 Bellaterra, Spain. E-mail: jlrodri{at}mat.uab.es |
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Abstract: | Our object of study is the natural tower which, for any givenmap f:AB and each space X, starts with the localization of Xwith respect to f and converges to X itself. These towers canbe used to produce approximations to localization with respectto any generalized homology theory E*, yielding, for example,an analogue of Quillen's plus-construction for E*. We discussin detail the case of ordinary homology with coefficients inZ/p or Z1/p]. Our main tool is a comparison theorem for nullificationfunctors (that is, localizations with respect to maps of theform f:Apt), which allows us, among other things, to generalizeNeisendorfer's observation that p-completion of simply-connectedspaces coincides with nullification with respect to a Moorespace M(Z1/p], 1). |
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