Algebraic properties of quasi-finite complexes

• Autorzy: M. Cencelj , J. Dydak , J. Smrekar , A. Vavpetič , Ž. Virk
• Języki publikacji: EN

Abstrakty

EN

A countable CW complex K is quasi-finite (as defined by A. Karasev) if for every finite subcomplex M of K there is a finite subcomplex e(M) such that any map f: A → M, where A is closed in a separable metric space X satisfying XτK, has an extension g: X → e(M). Levin's results imply that none of the Eilenberg-MacLane spaces K(G,2) is quasi-finite if G ≠ 0. In this paper we discuss quasi-finiteness of all Eilenberg-MacLane spaces. More generally, we deal with CW complexes with finitely many nonzero Postnikov invariants.
Here are the main results of the paper:
Theorem 0.1. Suppose K is a countable CW complex with finitely many nonzero Postnikov invariants. If π₁(K) is a locally finite group and K is quasi-finite, then K is acyclic.
Theorem 0.2. Suppose K is a countable non-contractible CW complex with finitely many nonzero Postnikov invariants. If π₁(K) is nilpotent and K is quasi-finite, then K is extensionally equivalent to S¹.

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2007
• Tom: 197
• Numer: 1
• Strony: 67-80

Daty

wydano

2007

Twórcy

autor

M. Cencelj

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

autor

J. Dydak

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

autor

J. Smrekar

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

autor

A. Vavpetič

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

autor

Ž. Virk

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

Identyfikatory

DOI

10.4064/fm197-0-4