On the stable Hopf invariant

We provide a simplified approach to the the stable Hopf invariant.

We provide short elementary proofs of the Cartan Formula, the Composition Formula, and the Transfer formula.

In addition, when $\pi$ is a discrete group, we show how to extend these results to the stable category of $\pi$-spaces.

We also consider the extent to which the stable Hopf invariant is unique.