In the mathematics of manifolds and differential operators, the Atiyah–Singer index theorem states that for an elliptic differential operator on a compact manifold, the analytical index (closely related to the dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data). It includes many other important theorems (such as the Riemann–Roch theorem) as special cases, and has applications in theoretical physics. It was proved by Michael Atiyah and Isadore Singer in 1963.

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