Algebraic properties of quasi-finite complexes

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dc.creatorCencelj, M.
dc.creatorDydak, J.
dc.creatorSmrekar, J.
dc.creatorVavpetic, A.
dc.creatorVirk, Z.
dc.date2005-09-24
dc.date.accessioned2026-07-07T09:23:24Z
dc.date.available2026-07-07T09:23:24Z
dc.descriptionA 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 $f:A\to M$, where $A$ is closed in a separable metric space $X$ satisfying $XτK$, has an extension $g:X\to e(M)$. Levin's results imply that none of the Eilenberg-MacLane spaces $K(G,2)$ is quasi-finite if $G\ne 0$. 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: Suppose $K$ is a countable CW complex with finitely many nonzero Postnikov invariants. If $π_1(K)$ is a locally finite group and $K$ is quasi-finite, then $K$ is acyclic. Suppose $K$ is a countable non-contractible CW complex with finitely many nonzero Postnikov invariants. If $π_1(K)$ is nilpotent and $K$ is quasi-finite, then $K$ is extensionally equivalent to $S^1$.
dc.description13 pages
dc.identifierhttps://arxiv.org/abs/math/0509582
dc.identifierhttp://arxiv.org/abs/math/0509582
dc.identifierFund. Math. 197 (2007), 67-80
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155722
dc.subjectGeometric Topology
dc.subjectAlgebraic Topology
dc.subject54F45,55M10, 54C65
dc.titleAlgebraic properties of quasi-finite complexes
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