Atiyah–Singer index theorem

Atiyah–Singer index theorem
Field	Differential geometry
First proof by	Michael Atiyah and Isadore Singer
First proof in	1963
Consequences	Chern–Gauss–Bonnet theorem; Grothendieck–Riemann–Roch theorem; Hirzebruch signature theorem; Rokhlin's theorem

In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index (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 theorems, such as the Chern–Gauss–Bonnet theorem and Riemann–Roch theorem, as special cases, and has applications to theoretical physics.

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