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Algebraic properties of quasi-finite complexes

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Cencelj M., Dydak J., Smrekar J., Vavpetič A., Virk Ž.

Fundamenta Mathematicae

2007

tom 197

nr 1

67-80

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Cencelj M.

1 Dydak J.

1 Smrekar J.

1 Vavpetič A.

1 Virk Ž.

1 2007

Wyniki wyszukiwania

Algebraic properties of quasi-finite complexes