Hurewicz-Serre Theorem in extension theory
| dc.creator | Cencelj, M. | |
| dc.creator | Dydak, J. | |
| dc.creator | Mitra, A. | |
| dc.creator | Vavpetic, A. | |
| dc.date | 2006-03-31 | |
| dc.date.accessioned | 2026-07-07T07:07:26Z | |
| dc.date.available | 2026-07-07T07:07:26Z | |
| dc.description | 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 $XτK(H_k(L),k)$ for all $k\ge 1$, then $XτK(π_k(F),k)$ and $XτK(π_k(L),k)$ for all $k\ge 2$. \par {\bf Theorem}. Let $X$ be a metrizable space such that $\dim(X) < \infty$ or $X\in ANR$. Suppose $L$ is a nilpotent CW complex and $SP(L)$ is its infinite symmetric product. If $XτSP(L)$, then $XτL$ in the following cases: \begin{itemize} \item[a.] $H_1(L)$ is finitely generated. \item[b.] $H_1(L)$ is a torsion group. \end{itemize} | |
| dc.identifier | https://arxiv.org/abs/math/0603748 | |
| dc.identifier | http://arxiv.org/abs/math/0603748 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110389 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Geometric Topology | |
| dc.subject | 55M10, 54F45, 54C65 | |
| dc.title | Hurewicz-Serre Theorem in extension theory | |
| dc.type | text |