Poincaré–Hopf theorem
Teorema de Poincaré-Hopf
- Date
- 1926 · confidence low
- Place
- Berlin, Germany
- Credited to
- Heinz Hopf y Henri Poincaré
- Field
- Knowledge & symbols
What was discovered
A theorem in differential topology relating the zeros of a continuous vector field on a compact differentiable manifold to the Euler characteristic of that manifold; it generalizes Poincaré's index and was proved in its general form by Heinz Hopf.
What it led to
- Fundamental tool of differential topology and vector field theory
- Applications in physics (why a sphere cannot be combed without a cowlick)
- Basis for later developments in algebraic topology