Geodesic
Cores of spaces, spectra, and $E_{\infty}$ ring spectra
Homology, homotopy, and applications, Tome 3 (2001) no. 2, pp. 341-354.

Voir la notice de l'article provenant de la source International Press of Boston

In a paper that has attracted little notice, Priddy showed that the Brown-Peterson spectrum at a prime $p$ can be constructed from the $p$-local sphere spectrum $S$ by successively killing its odd dimensional homotopy groups. This seems to be an isolated curiosity, but it is not. For any space or spectrum $Y$ that is $p$-local and $(n_0-1)$-connected and has $\pi_{n_0}(Y)$ cyclic, there is a $p$-local, $(n_0-1)$-connected “nuclear” CW complex or CW spectrum $X$ and a map $f: X\to Y$ that induces an isomorphism on $\pi_{n_0}$ and a monomorphism on all homotopy groups. Nuclear complexes are atomic: a self-map that induces an isomorphism on $\pi_{n_0}$ must be an equivalence. The construction of $X$ from $Y$ is neither functorial nor even unique up to equivalence, but it is there. Applied to the localization of $MU$ at $p$, the construction yields $BP$.
DOI : 10.4310/HHA.2001.v3.n2.a3
Classification : 55P15, 55P42, 55P43, 55S12
Keywords: atomic space, Brown-Peterson spectrum, localization, Einfty ring spectrum 
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P. Hu; I. Kriz; J. P. May. Cores of spaces, spectra, and $E_{\infty}$ ring spectra. Homology, homotopy, and applications, Tome 3 (2001) no. 2, pp. 341-354. doi : 10.4310/HHA.2001.v3.n2.a3. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2001.v3.n2.a3/

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