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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Localizing with respect to self-maps of the circle
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by Carles Casacuberta and Georg Peschke PDF
Trans. Amer. Math. Soc. 339 (1993), 117-140 Request permission

Abstract:

We describe a general procedure to construct idempotent functors on the pointed homotopy category of connected ${\text {CW}}$-complexes, some of which extend $P$-localization of nilpotent spaces, at a set of primes $P$. We focus our attention on one such functor, whose local objects are ${\text {CW}}$-complexes $X$ for which the $p$th power map on the loop space $\Omega X$ is a self-homotopy equivalence if $p \notin P$. We study its algebraic properties, its behaviour on certain spaces, and its relation with other functors such as Bousfield’s homology localization, Bousfield-Kan completion, and Quillen’s plus-construction.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 339 (1993), 117-140
  • MSC: Primary 55P60; Secondary 18G99, 20J05, 55N25, 55P10
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1123451-X
  • MathSciNet review: 1123451