The paper is devoted to generalizations of the Cencelj-Dranishnikov theorems relating extension properties of nilpotent CW complexes to their homology groups. Here are the main results of the paper: Theorem 0.1. Let L be a nilpotent CW complex and F the homotopy fiber of the inclusion i of L into its infinite symmetric product SP(L). If X is a metrizable space such that for all k ≥ 1, then and for all k ≥ Theorem 0.2. Let X be a metrizable space such that dim(X) < ∞ or X ∈ ANR. Suppose L is a nilpotent CW complex. If XτSP(L), then XτL in the following cases: (a) H₁(L) is finitely generated. (b) H₁(L) is a torsion group.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-2-2,
author = {M. Cencelj and J. Dydak and A. Mitra and A. Vavpeti\v c},
title = {Hurewicz-Serre theorem in extension theory},
journal = {Fundamenta Mathematicae},
volume = {201},
year = {2008},
pages = {113-123},
zbl = {1151.54027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-2-2}
}
M. Cencelj; J. Dydak; A. Mitra; A. Vavpetič. Hurewicz-Serre theorem in extension theory. Fundamenta Mathematicae, Tome 201 (2008) pp. 113-123. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-2-2/