Open Access
Translator Disclaimer
2001 Cores of spaces, spectra, and {$E\sb \infty$} ring spectra
P. Hu, I. Kriz, J. P. May
Homology Homotopy Appl. 3(2): 341-354 (2001).


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 $BP$.


Download Citation

P. Hu. I. Kriz. J. P. May. "Cores of spaces, spectra, and {$E\sb \infty$} ring spectra." Homology Homotopy Appl. 3 (2) 341 - 354, 2001.


Published: 2001
First available in Project Euclid: 13 February 2006

zbMATH: 0987.55009
MathSciNet: MR1856030

Primary: 55P15
Secondary: 55P43

Rights: Copyright © 2001 International Press of Boston


Vol.3 • No. 2 • 2001
Back to Top