2006/03/31 by Matija Cencelj, Jerzy Dydak, Cencelj, M. +5
Mathematics · #54C65 #54F45 #55M10 #Advanced Topics in Algebra #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.math/0603748
openalex publication_date 2006/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper is devoted to generalizations of Cencelj-Dranishnikov theorems relating extension properties of nilpotent CW complexes to its homology groups. Here are the main results of the paper: \par \bf Theorem. Suppose L is a nilpotent CW complex and F is the homotopy fiber of the inclusion i of L into its infinite symmetric product SP(L). If X is a metrizable space such that XτK(Hk(L),k) for all k≥ 1, then XτK(πk(F),k) and XτK(πk(L),k) for all k≥ 2. \par \bf Theorem. Let X be a metrizable space such that dim(X) < ∞ or X∈ ANR. Suppose L is a nilpotent CW complex and SP(L) is its infinite symmetric product. If XτSP(L), then XτL in the following cases: \beginitemize \item[a.] H1(L) is finitely generated. \item[b.] H1(L) is a torsion group. \enditemize