On the Hopf-James homomorphism over B

Abstract

We define the Hopf-James homomorphism and the Whitehead product in the category of fibrewise pointed spaces over B. Making use of them, we generalize Hardie-Jansen's result [6] and obtain that a version of the generalized Hopf construction gives rise to an element which can be detected by a generalized Hopf invariant under some conditions.

Keywords: Fibrewise, Hopf-James homomorphism, Whitehead product

Quaestiones Mathematicae 31(2008), 1–9