Hurewicz-Serre theorem in extension theory

• Autorzy: M. Cencelj , J. Dydak , A. Mitra , A. Vavpetič
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 55M10: Dimension theory
• 54C65: Selections
• 54F45: Dimension theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 198
• Numer: 2
• Strony: 113-123

Daty

wydano

2008

Twórcy

autor

M. Cencelj

• IMFM, Univerza v Ljubljani, Jadranska ulica 19, SI-1111 Ljubljana, Slovenija

autor

J. Dydak

• University of Tennessee, Knoxville, TN 37996, U.S.A.

autor

A. Mitra

• University of Tennessee, Knoxville, TN 37996, U.S.A.

autor

A. Vavpetič

• Fakulteta za Matematiko in Fiziko, Univerza v Ljubljani, Jadranska ulica 19, SI-1111 Ljubljana, Slovenija

Identyfikatory

DOI

10.4064/fm198-2-2