Homotopy groups of spheres correspond to framed submanifolds of Euclidean space through the Pontrjagin-Thom construction. For example, the Hopf map corresponds to a circle in $\mathbb{R}^3$ 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.

Homotopy groups of spheres correspond to framed submanifolds of Euclidean space through the Pontrjagin-Thom construction. For example, the Hopf map corresponds to a circle in $\mathbb{R}^3$ framed “with a twist”. The homotopy groups of $S^1$ thus correspond to framed codimension one submanifolds. But such are canonically framed and all bound, so there are no interesting/ non-trivial examples.

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.

Homotopy groups of spheres correspond to framed submanifolds of Euclidean space through the Pontrjagin-Thom construction. For example, the Hopf map corresponds to a circle in $\mathbb{R}^3$ 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.