 Degree of a continuous mapping

For a map $f:S^m\to S^m$, the degree is the integer by which $f_{\ast }$ multiplies a chosen generator of $H_m(S^m;\mathbb{Z})$. It is invariant under homotopy.

The degree of a continuous mapping refers to a topological invariant that describes the number of times a continuous function covers its target space. This concept is most commonly applied in the context of mappings between spheres or between manifolds.