%0 Journal Article
%T Yet another Hopf Invariant
%A Jean-Paul Doeraene
%A Mohammed El Haouari
%J Mathematics
%D 2015
%I arXiv
%X The classical Hopf invariant is defined for a map f: S^r -> X. Here we define `hcat' which is some kind of Hopf invariant built with a construction in Ganea's style, valid for maps not only on spheres but more generally on a `relative suspension' f: Sigma_A W -> X. We study the relation between this invariant and the sectional category and the relative category of a map. In particular, for f being the `restriction' of f on A, we have relcat(i) <= hcat(f) <= relcat(i) + 1 and relcat(f) <= hcat(f).
%U http://arxiv.org/abs/1501.03712v4