Yet another Hopf Invariant
Algebraic Topology
2025-03-18 v4
Abstract
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).
Cite
@article{arxiv.1501.03712,
title = {Yet another Hopf Invariant},
author = {Jean-Paul Doeraene and Mohammed El Haouari},
journal= {arXiv preprint arXiv:1501.03712},
year = {2025}
}