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.
Formal statement
Let M be an n-dimensional compact oriented manifold and Sn the n-sphere and be continuous. Then if and only if f and g are homotopic.
References
- Milnor, J. W. (1997). Topology from the Differentiable Viewpoint. Princeton University Press. ISBN 978-0-691-04833-8.
- Enrique Outerelo, Jesús M. Ruiz (2009). Mapping degree theory. AMS. ISBN 978-0-8218-4915-6.