Hopf theorem

The Hopf theorem is a statement in differential topology, saying that the topological degree is the only homotopy invariant of continuous maps to spheres.Let M be an n-dimensional compact oriented manifold and Sn the n-sphere and f , g : M → S n {displaystyle f,g:M o S^{n}}   be continuous. Then deg ⁡ ( f ) = deg ⁡ ( g ) {displaystyle deg(f)=deg(g)}   if and only if f and g are homotopic.