Finite-dimensional spaces in resolving classes

Jeffrey Strom¹

¹ Department of Mathematics Western Michigan University Kalamazoo, MI 49008-5200, U.S.A.

Fundamenta Mathematicae, Tome 217 (2012) no. 2, pp. 171-187

Résumé

Using the theory of resolving classes, we show that if $X$ is a CW complex of finite type such that ${\rm map}_*(X, S^{2n+1})\sim *$ for all sufficiently large $n$, then ${\rm map}_*(X, K) \sim *$ for every simply-connected finite-dimensional CW complex $K$; and under mild hypotheses on $\pi_1(X)$, the same conclusion holds for all finite-dimensional complexes $K$. Since it is comparatively easy to prove the former condition for $X = B\mathbb Z/p$ (we give a proof in an appendix), this result can be applied to give a new, more elementary proof of the Sullivan conjecture.

Détail

DOI : 10.4064/fm217-2-3

Keywords: using theory resolving classes complex finite type map * sim * sufficiently large map * sim * every simply connected finite dimensional complex under mild hypotheses conclusion holds finite dimensional complexes since comparatively easy prove former condition mathbb proof appendix result applied elementary proof sullivan conjecture