I have a map, constructed geometrically, $S^4 \to S^3$. I suspect that it is a representative for the generator $\eta_3\in \pi_4(S^3) \simeq \mathbb{Z}_2$, but I am not 100% sure ($\eta_3$ is defined as the suspension of the Hopf map $S^3 \to S^2$). I'd like to be able to detect the fact that my map is homotopically nontrivial in a geometric or combinatorial way. Is this possible? I imagine there is some sort of index one can calculate, but unfortunately the terms one looks these things up in are very generic (forms, integration, index etc).