Miller spaces and spherical resolvability of finite complexes

• Autorzy: Jeffrey Strom
• Języki publikacji: EN

Abstrakty

EN

Let 𝒜 be a fixed collection of spaces, and suppose K is a nilpotent space that can be built from spaces in 𝒜 by a succession of cofiber sequences. We show that, under mild conditions on the collection 𝒜, it is possible to construct K from spaces in 𝒜 using, instead, homotopy (inverse) limits and extensions by fibrations. One consequence is that if K is a nilpotent finite complex, then ΩK can be built from finite wedges of spheres using homotopy limits and extensions by fibrations. This is applied to show that if map⁎(X,Sⁿ) is weakly contractible for all sufficiently large n, then map⁎(X,K) is weakly contractible for any nilpotent finite complex K.

Kategorie tematyczne

• 55P50: String topology
• 55Q05: Homotopy groups, general; sets of homotopy classes

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 178
• Numer: 2
• Strony: 97-108

Daty

wydano

2003

Twórcy

autor

Jeffrey Strom

• Western Michigan University, Kalamazoo, MI 49008, U.S.A.

Identyfikatory

DOI

10.4064/fm178-2-1