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ON TOWERS APPROXIMATING HOMOLOGICAL LOCALIZATIONS

Published online by Cambridge University Press:  01 December 1997

CARLES CASACUBERTA  and
JOSÉ L. RODRÍGUEZ
CARLES CASACUBERTA
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain. E-mail: [email protected], [email protected]
JOSÉ L. RODRÍGUEZ
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain. E-mail: [email protected], [email protected]
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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).

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 56 , Issue 3 , December 1997 , pp. 645 - 656
Copyright
The London Mathematical Society 1997

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