How to write a 4-form of topological charge which would correspond to non-zero element of the homotopy group $\pi_4(S^3)$ or $\pi_4(S^2)$ (both are equal to $Z_2$) ? ?

An example of such a mapping (non-trivial), or even a homotopy of maps ($0\leq \tau\le 1$), is (or `localized' maps $R^4=H \to S^3$)

$f(h) = \frac{q-1}{q+1}$, where $q=h\ i\ \bar{h}+\tau\ i$ ;

here $h$ - quaternion, $q$ - imaginary quaternion, $f\in S^3$ - quaternion of unit length.

Motivation: to describe topological charges (and quasi-charges) in the frame field theory (or Absolute Parallelism), see arXiv: gr-qc/0610076 .