Poincaré-Hopf theorem
where index(v;pi) denotes the index of the singularity at pi and χ(X) denotes the Euler charactertistic of X. The theorem implies the hairy ball theorem. Heinz Hopf later generalized the theorem to higher-dimensional manifolds.
A flow on a sphere
In the figure is a sphere with sink (index 1) at north pole and source (index 1) at south pole giving. χ = 2.
- Dirichlet function
- Dirichlet, Peter Gustav Lejeune
- Dirichlet problem
- Dirichlet's approximation theorem
- Dirichlet series
- Dirichlet's test
- disc
- disc of convergence
- disconnected
- discontinuity
- discontinuous function
- discrete
- discrete data
- discrete Fourier transform
- discrete logarithm
- discrete mathematics
- discrete metric
- discrete random variable
- discrete space
- discretization
- discriminant
- discriminatory
- disjoint
- disjoint union
- disjunction