Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Localizing with respect to self-maps of the circle
HTML articles powered by AMS MathViewer

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.
References
Similar Articles
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