Localizing groups with action
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In this paper, it was shown that the loop space of a connected CW-complex is a P-local group, up to homotopy, if and only if p1X and the free homotoopy groups [Sk-1, OX], k = 2, are p-local.Abstract:
When localizing the semidirect product of two groups, the effect on the factors is made explicit. As an application in Topology, we show that the loop space of a based connected CW-complex is a P-local group, up to homotopy, if and only if p1X and the free homotopy groups [Sk-1, OX], k = 2, are P-local.read more
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Journal ArticleDOI
Localizing with respect to self-maps of the circle
Carles Casacuberta,Georg Peschke +1 more
TL;DR: In this article, the authors describe a general procedure to construct idempotent functors on the pointed homotopy category of connected CW-complexes, some of which extend /"-localization of nilpotent spaces, at a set of primes P.
Book ChapterDOI
Adams Memorial Symposium on Algebraic Topology: On orthogonal pairs in categories and localization
TL;DR: In this paper, the authors give conditions on the category C and the class of morphismsM ensuring the reflectivity of D, sometimes even providing an explicit construction of the left adjoint E : C → D; see for example Adams[1], Bousfield [3]-4], Deleanu-Frei-Hilton [9][10], Heller [15], Yosimura [22], Dror-Farjoun [11], Kelly [12].
Journal ArticleDOI
Localization methods in the study of the homology of virtually nilpotent groups
TL;DR: In a series of papers [13, 14, 15], Hilton introduced the terminology relative group to denote a group epimorphism ∈:G↠Q, and relative space to represent a map between connected spaces inducing an epimomorphism of fundamental groups as discussed by the authors.
References
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Homotopy Limits, Completions and Localizations
A. K. Bousfield,Daniel M. Kan +1 more
TL;DR: The main purpose of part I of these notes is to develop for a ring R a functional notion of R-completion of a space X, which coincides up to homotopy with the p-profinite completion of Quillen and Sullivan as mentioned in this paper.
Journal ArticleDOI
Some aspects of groups with unique roots
TL;DR: In this paper, the authors define a set of genera liers a nd genera ies of U-group, E-group and D-group groups, which are used to define local groups.
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