Let 𝒜 be a fixed collection of spaces, and suppose K is a nilpotent space that can be built from spaces in 𝒜 by a succession of cofiber sequences. We show that, under mild conditions on the collection 𝒜, it is possible to construct K from spaces in 𝒜 using, instead, homotopy (inverse) limits and extensions by fibrations. One consequence is that if K is a nilpotent finite complex, then ΩK can be built from finite wedges of spheres using homotopy limits and extensions by fibrations. This is applied to show that if map⁎(X,Sⁿ) is weakly contractible for all sufficiently large n, then map⁎(X,K) is weakly contractible for any nilpotent finite complex K.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm178-2-1,
author = {Jeffrey Strom},
title = {Miller spaces and spherical resolvability of finite complexes},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {97-108},
zbl = {1052.55015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm178-2-1}
}
Jeffrey Strom. Miller spaces and spherical resolvability of finite complexes. Fundamenta Mathematicae, Tome 177 (2003) pp. 97-108. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm178-2-1/