A strong-shape theoretical version of a result due to E. Lima
type: Item
instance of: scholarly article
title: A strong-shape theoretical version of a result due to E. Lima
zbMATH Open document ID: 0724.55005
DOI: 10.1016/0166-8641(91)90055-Q
published in: Topology and its Applications
publication date: 1991-01-01T00:00:00Z
review text: The S-duality or Spanier-Whitehead duality has been adequately transformed and proved in both shape theoretic setting and strong shape theoretic setting. In fact, the shape theoretic version has been proved, prior to the development of shape theory, by \textit{E. L. Lima} [Summa Brasil. Math. 4, 91-147 (1959; Zbl 0102.383)] and later, independently, by \textit{S. Nowak} [Fundam. Math. 128, 47-60 (1987; Zbl 0633.55009)], while the strong shape theoretic version is proved by \textit{Q. Haxhibeqiri} and \textit{S. Nowak} [Duality between stable strong shape morphisms and stable homotopy classes, Glas. Mat., III. Ser. (to appear)], and this theorem has been announced by the same authors in their paper ``Stable strong shape theory'' [ibid. 24(44), 149-160 (1989; Zbl 0682.55007)]. This theorem states that the stable strong shape category of subcompacta of the n-sphere is isomorphic to the stable homotopy category of their complements. The author of the reviewed paper proves this as a consequence of his results obtained in his previous paper ``Duality in manifolds'' [Ann. Mat. Pura Appl. IV. Ser. 136, 241- 302 (1974; Zbl 0564.55001)].
reviewed by: Ivan Ivanšić
Mathematics Subject Classification ID: 55P25
Mathematics Subject Classification ID: 55P55
Mathematics Subject Classification ID: 55M05
zbMATH DE Number: 4194699
zbMATH Keywords: S-duality
zbMATH Keywords: Spanier-Whitehead duality
zbMATH Keywords: shape
zbMATH Keywords: strong shape
zbMATH Keywords: stable strong shape category
author: Friedrich Wilhelm Bauer
MaRDI profile type: Publication
cites work: Duality in manifolds
cites work: Homotopical approach to strong shape or completion theory
cites work: Cech and Steenrod homotopy theories with applications to geometric topology
cites work: Q3286061
cites work: On the relationships between shape properties of subcompacta of $S^n$ and homotopy properties of their complements
full work available at URL: 0166-8641(91)90055-q
OpenAlex ID: W1978820210
Wikidata QID: Q127957351
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description: scientific article; zbMATH DE number 4194699