Hopf theorem

Let M be an n-dimensional compact connected oriented manifold and ${\displaystyle S^{n}}$  the n-sphere and ${\displaystyle f,g\colon M\to S^{n}}$  be continuous. Then ${\displaystyle \deg(f)=\deg(g)}$  if and only if f and g are homotopic.

• Milnor, John W. (1997). Topology from the Differentiable Viewpoint. Princeton University Press. ISBN 978-0-691-04833-8.