Hopf–Ganea invariants and weak LS category

In this work, we recall the definition of Hopfʹs invariants given by Ganea and we define a Hopf invariant adapted to a cone decomposition of a space. As Berstein and Hilton did, we apply it for the computation of the weak category of Lusternik and Schnirelmann of a space. An example provided by the cellular decomposition of Sp(3) shows the efficiency of this method.