Finite-dimensional spaces in resolving classes

Jeffrey Strom. "Finite-dimensional spaces in resolving classes." Fundamenta Mathematicae 217.2 (2012): 171-187. <http://eudml.org/doc/282666>.

@article{JeffreyStrom2012,
abstract = {Using the theory of resolving classes, we show that if X is a CW complex of finite type such that $map⁎(X,S^\{2n+1\}) ~ ∗$ 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.},
author = {Jeffrey Strom},
journal = {Fundamenta Mathematicae},
keywords = {Sullivan conjecture; resolving class; resolving kernel; homotopy limit; cone length; phantom map; Massey-Peterson tower; T functor; Steenrod algebra; unstable module},
language = {eng},
number = {2},
pages = {171-187},
title = {Finite-dimensional spaces in resolving classes},
url = {http://eudml.org/doc/282666},
volume = {217},
year = {2012},
}

TY - JOUR
AU - Jeffrey Strom
TI - Finite-dimensional spaces in resolving classes
JO - Fundamenta Mathematicae
PY - 2012
VL - 217
IS - 2
SP - 171
EP - 187
AB - Using the theory of resolving classes, we show that if X is a CW complex of finite type such that $map⁎(X,S^{2n+1}) ~ ∗$ 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.
LA - eng
KW - Sullivan conjecture; resolving class; resolving kernel; homotopy limit; cone length; phantom map; Massey-Peterson tower; T functor; Steenrod algebra; unstable module
UR - http://eudml.org/doc/282666
ER -