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Finite-dimensional spaces in resolving classes

Jeffrey Strom (2012)

Fundamenta Mathematicae

Using the theory of resolving classes, we show that if X is a CW complex of finite type such that m a p ( X , S 2 n + 1 ) 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....

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