Hopf theorem - Alchetron, The Free Social Encyclopedia

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 f , g : M → S n be continuous. Then deg ⁡ ( f ) = deg ⁡ ( g ) if and only if f and g are homotopic.

References

Hopf theorem Wikipedia

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