"Atiyah-Singer index theorem" meaning in All languages combined

{
  "etymology_text": "Proved by Michael Atiyah and Isadore Singer in 1963.",
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      "glosses": [
        "A theorem stating 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)."
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        "(differential geometry) A theorem stating 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)."
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{
  "etymology_text": "Proved by Michael Atiyah and Isadore Singer in 1963.",
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        "A theorem stating 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)."
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        "(differential geometry) A theorem stating 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)."
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