A strong shape theory with S-duality

• Autorzy: Friedrich W. Bauer
• Języki publikacji: EN

Abstrakty

EN

If in the classical S-category $\frakP$, 1)$ continuous mappings are replaced by compact-open strong shape (= {coss}) morphisms (cf. §1 or [1], §2), and 2) ∧-products are properly reinterpreted, then an S-duality theorem for arbitrary subsets $X ⊂ S^n$ (rather than for compact polyhedra) holds (Theorem 2.1).

Słowa kluczowe

EN

S-duality; Alexander duality; compact-open strong shape; virtual spaces

Kategorie tematyczne

• 55P55: Shape theory
• 55P25: Spanier-Whitehead duality
• 55N20: Generalized (extraordinary) homology and cohomology theories
• 55N05: \v Cech types

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1997
• Tom: 154
• Numer: 1
• Strony: 37-56

Daty

wydano

1997

otrzymano

1996-01-25

Twórcy

autor

Friedrich W. Bauer

• Fachbereich Mathematik, Johann-Wolfgang-Goethe Universität, Robert-Mayer Str. 6-10, 60054 Frankfurt a.M. 11, Germany

Bibliografia

• [1] F. W. Bauer, A strong shape theory admitting an S-dual, Topology Appl. 62 (1995), 207-232.
• [2] F. W. Bauer, A strong-shape theoretical version of a result due to E. Lima, Topology Appl. 40 (1991), 17-21.
• [3] F. W. Bauer, Duality in manifolds, Ann. Mat. Pura Appl. (4) 136 (1984), 241-302.
• [4] J. M. Boardman, Stable homotopy is not self-dual, Proc. Amer. Math. Soc. 26 (1970), 369-370.
• [5] O. Hanner, Some theorems on absolute neighborhood retracts, Ark. Mat. 1 (1952), 389-408.
• [6] Q. Haxhibeqiri and S. Nowak, Duality between stable strong shape morphisms and stable homotopy classes, Glas. Mat., to appear.
• [7] E. Lima, The Spanier-Whitehead duality in new homotopy categories, Summa Brasil. Math. 4 (1959), 91-148.
• [8] T. Y. Lin, Duality and Eilenberg-MacLane spectra, Proc. Amer. Math. Soc. 56 (1976), 291-299.
• [9] H. R. Margolis, Spectra and the Steenrod Algebra, North-Holland Math. Library 29, North-Holland, 1983.
• [10] E. Spanier, Algebraic Topology, McGraw-Hill, 1966.