Homotopy groups of n-spheres are about embedding n-spheres into a manifold of dimension k.
I want to understand what does operationally mean $\pi_n (S^k)$ when $n >k$. The definition of embedding i'm familiar with requires that the embedded manifold (in this case n-spheres) are always lower or equally dimensional.
In short, i don't have any intuition whatsoever what does it mean to embed a 2-sphere inside, say, a 1-sphere (a loop). What kind of mapping would that be?