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Hopf theorem

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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 978-0691048338.
  • Enrique Outerelo, Jesús M. Ruiz (2009). Mapping degree theory. AMS. ISBN 978-0821849156.