High Quality Content by WIKIPEDIA articles! In mathematics, the Poincare–Hopf theorem (also known as the Poincare–Hopf index formula, Poincare–Hopf index theorem, or Hopf index theorem) is an important theorem in differential topology. It is named after Henri Poincare and Heinz Hopf. The Poincare–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 a sphere having no sources or sinks.

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