"Atiyah-Singer index theorem" meaning in English

{
  "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",
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          "elliptic differential operator",
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          "topological",
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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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        "Atiyah-Singer index theorem"
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{
  "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",
          "differential geometry"
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          "compact"
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          "manifold",
          "manifold"
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          "dimension"
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          "space"
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      "raw_glosses": [
        "(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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