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Localizing with respect to self-maps of the circle
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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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CASACUBERTA, Carles and PESCHKE, Georg. Localizing with respect to self-maps of the circle. Transactions of the American Mathematical Society. 1993. Vol. 339, num. 1, pags. 117-140. ISSN 0002-9947. [consulted: 20 of August of 2026]. Available at: https://hdl.handle.net/2445/96481