Fibrewise Decomposition of Generalized Suspension Spaces and Loop Spaces

  • Nobuyuki Oda

    Fukuoka University, Japan

Abstract

We work in the category of fibrewise pointed topological spaces over . Let be a co-Hopf space (which need not be co-associative) in . The -suspension space and the -loop space of a fibrewise pointed space over are defined as generalization of the usual suspension space and the loop space respectively, -suspension spaces and -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 -suspension space and -loop space are proved. Short exact sequences of homotopy sets involving -suspension spaces or -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. 281–295

DOI 10.2977/PRIMS/1195166134