Poincaré–Hopf theorem
Counts 0s of a vector field on a differentiable manifold using its Euler characteristic / From Wikipedia, the free encyclopedia
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In mathematics, the Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem) is an important theorem that is used in differential topology. It is named after Henri Poincaré and Heinz Hopf.
The Poincaré–Hopf theorem is often illustrated by the special case of the hairy ball theorem, which simply states that there is no smooth vector field on an even-dimensional n-sphere having no sources or sinks.