Abelian and non-Abelian Hopfions in all odd dimensions

We extend the definition of the topological charge pertaining to the CP1 (i.e. O(3)) Skyrme-Fadde'ev Hopfion on 3 to candidates for topological charges of Pn sigma models on 2n+1 for all n. For this, the Abelian composite connections of the Pn sigma models are employed. In higher dimensions (n ≥ 1) it turns out that such charges, described by the nonAbelian composite connections of suitable Grassmannian sigma models, can also be constructed. A concrete discussion of the non-Abelian case for n 2 is presented.