Poincaré Hopf Theorem
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 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 a sphere having no sources or sinks.

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 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 a sphere having no sources or sinks.