Poincaré-Hopf Index Theorem

The index of a vector field with finitely many zeros on a compact, oriented manifold is the same as the Euler characteristic of the manifold.

See also

Gauss-Bonnet Formula

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Cite this as:

Weisstein, Eric W. "Poincaré-Hopf Index Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Poincare-HopfIndexTheorem.html

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