Sejam $h: S^{3} \to S^{2}$ the Hopf fibration, its induced a sequence exact of homotopy groups, given by
$$\cdots \to \pi_{n}(S^1) \to \pi_{n}(S^3) \to \pi_{n}(S^2) \to \pi_{n-1}(S^1) \to \cdots $$
for $n \geq 3$, we have isomorphism $\pi_{3}(S^3) \cong \pi_{3}(S^2) \cong \mathbb{Z}$. I can show that $\pi_{3}(S^2)$ is generated by Hopf Fibration and it has relationship with Hopf Invariant wich is equal 1. I'm taking the Hopf Invariant as the linking number between two curves, it has relationship with the generator of homotopy groups. I would like to know someone know books or something with theorey about this relationship between Hopf Invariant, linking number and homotopy groups of sphere, without cohomology and integration.
I would say check in Steenrod's The Topology of Fibre Bundles, 1951, Princeton University Press.