# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Hurewicz–Serre theorem in extension theory

### Tom 198 / 2008

Fundamenta Mathematicae 198 (2008), 113-123 MSC: Primary 54F45; Secondary 55M10, 54C65. DOI: 10.4064/fm198-2-2

#### Streszczenie

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 $X\tau K(H_k(L),k)$ for all $k\ge 1$, then $X\tau K(\pi_k(F),k)$ and $X\tau K(\pi_k(L),k)$ for all $k\ge 2$.
Theorem 0.2. Let $X$ be a metrizable space such that ${\mathop{\rm dim}}(X) < \infty$ or $X\in ANR$. Suppose $L$ is a nilpotent CW complex. If $X\tau SP(L)$, then $X\tau L$ in the following cases$:$

(a) $H_1(L)$ is finitely generated.

(b) $H_1(L)$ is a torsion group.

#### Autorzy

• M. CenceljIMFM
Univerza v Ljubljani
SI-1111 Ljubljana, Slovenija
e-mail
• J. DydakUniversity of Tennessee
Knoxville, TN 37996, U.S.A.
e-mail
• A. MitraUniversity of Tennessee
Knoxville, TN 37996, U.S.A.
e-mail
• A. VavpetičFakulteta za Matematiko in Fiziko
Univerza v Ljubljani