Hurewicz-Serre theorem in extension theory

M. Cencelj; J. Dydak; A. Mitra; A. Vavpetič

Fundamenta Mathematicae (2008)

  • Volume: 198, Issue: 2, page 113-123
  • ISSN: 0016-2736

Abstract

top
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 τ K ( H k ( L ) , k ) for all k ≥ 1, then X τ K ( π k ( F ) , k ) and X τ K ( π k ( L ) , k ) 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.

How to cite

top

M. Cencelj, et al. "Hurewicz-Serre theorem in extension theory." Fundamenta Mathematicae 198.2 (2008): 113-123. <http://eudml.org/doc/282814>.

@article{M2008,
abstract = {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 $XτK(H_\{k\}(L),k)$ for all k ≥ 1, then $XτK(π_\{k\}(F),k)$ and $XτK(π_\{k\}(L),k)$ 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.},
author = {M. Cencelj, J. Dydak, A. Mitra, A. Vavpetič},
journal = {Fundamenta Mathematicae},
keywords = {extension dimension; cohomological dimension; absolute extensor; nilpotent groups},
language = {eng},
number = {2},
pages = {113-123},
title = {Hurewicz-Serre theorem in extension theory},
url = {http://eudml.org/doc/282814},
volume = {198},
year = {2008},
}

TY - JOUR
AU - M. Cencelj
AU - J. Dydak
AU - A. Mitra
AU - A. Vavpetič
TI - Hurewicz-Serre theorem in extension theory
JO - Fundamenta Mathematicae
PY - 2008
VL - 198
IS - 2
SP - 113
EP - 123
AB - 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 $XτK(H_{k}(L),k)$ for all k ≥ 1, then $XτK(π_{k}(F),k)$ and $XτK(π_{k}(L),k)$ 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.
LA - eng
KW - extension dimension; cohomological dimension; absolute extensor; nilpotent groups
UR - http://eudml.org/doc/282814
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.