Using the theory of resolving classes, we show that if X is a CW complex of finite type such that for all sufficiently large n, then map⁎(X,K) ∼ ∗ for every simply-connected finite-dimensional CW complex K; and under mild hypotheses on π₁(X), the same conclusion holds for all finite-dimensional complexes K. Since it is comparatively easy to prove the former condition for X = Bℤ/p (we give a proof in an appendix), this result can be applied to give a new, more elementary proof of the Sullivan conjecture.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm217-2-3,
author = {Jeffrey Strom},
title = {Finite-dimensional spaces in resolving classes},
journal = {Fundamenta Mathematicae},
volume = {219},
year = {2012},
pages = {171-187},
zbl = {1251.55010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm217-2-3}
}
Jeffrey Strom. Finite-dimensional spaces in resolving classes. Fundamenta Mathematicae, Tome 219 (2012) pp. 171-187. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm217-2-3/