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arXiv · 1501.03712

Yet another Hopf Invariant

Jean-Paul Doeraene·Mohammed El Haouari
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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).

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Jean-Paul Doeraene, Mohammed El Haouari. 2015-01-15. Yet another Hopf Invariant. https://doi.org/10.13140/rg.2.1.2295.0883

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