We work in the category TopBB of fibrewise pointed topological spaces over B. Let Γ be a co-Hopf space (which need not be co-associative) in TopBB. The ΓB-suspension space ΓBX and the ΓB-loop space Γ*BX of a fibrewise pointed space X over B are defined as generalization of the usual suspension space ΣX and the loop space ΩX respectively, ΓB-suspension spaces and ΓB-loop spaces have some properties similar to those of the usual suspension spaces and loop spaces. This is an example of Eckmann-Hilton duality. In this paper, decomposition theorems of ΓB-suspension space ΓBX and ΓB-loop space Γ*BX are proved. Short exact sequences of homotopy sets involving ΓB-suspension spaces or ΓB-loop spaces are obtained in the category of algebraic loops.
Cite this article
Nobuyuki Oda, Fibrewise Decomposition of Generalized Suspension Spaces and Loop Spaces. Publ. Res. Inst. Math. Sci. 30 (1994), no. 2, pp. 281–295DOI 10.2977/PRIMS/1195166134