Degree of self-maps of spheres

Remark 2.4.20 (Degree). For every \(n\geq 1\), the degree of a self-map of the \(n\)-sphere induces an isomorphism \[ \deg \colon \pi _n(S^n) \xrightarrow {\cong } \Z . \] Under these isomorphisms, suspension preserves degree. In particular, a pointed self-map of \(S^n\) is pointed homotopic to the identity if and only if it has degree \(1\).