Homotopy groups of spheres correspond to framed submanifolds of Euclidean space through the Pontjagin-Thom construction. For example, the Hopf map corresponds to a circle framed “with a twist”. The homotopy groups of $S^1$ thus correspond to framed codimension one submanifolds. But such are canonically framed, so there are no interesting/ non-trivial examples.
Dev Sinha
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