Atiyah–Singer index theorem
Mathematical result in differential geometry / From Wikipedia, the free encyclopedia
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In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963),[1] 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.[2][3]
Quick Facts Field, First proof by ...
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 |
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