Original scientific paper

Duality between stable strong shape morphisms and stable homotopy classes

Qamil Haxhibeqiri
Slawomir Nowak

Abstract

Let SStrShn be the full subcategory of the stable strong shape category SStrSh of pointed compacta whose objects are all pointed subcompacta of Sn and let SOn be the full subcategory of the stable homotopy category S whose objects are all open subsets of Sn. In this paper it is shown that there exists a contravariant additive functor Dn : SStrShn → SOn such that Dn(X) = Sn \ X for every subcompactum X of Sn and Dn : SStrShn(X, Y) → SOn(Sn \ Y, Sn \ X) is an isomorphism of abelian groups for all compacta X, Y ⊂ Sn. Moreover, if X ⊂ Y ⊂ Sn, j : Sn \ Y → Sn \ X is an inclusion and α ∈ SStrShn(X, Y) is induced by the inclusion of X into Y then Dn(α) = {j}.

Keywords

Stable strong shape; stable homotopy; proper map; proper homotopy

Hrčak ID:

4842

URI

https://hrcak.srce.hr/4842

Publication date:

1.12.2001.

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