"Hodge theory" meaning in English

{
  "etymology_text": "Named after W. V. D. Hodge.",
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  "lang_code": "en",
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        "One aspect of the study of differential forms of a smooth manifold M. More specifically, it works out the consequences for the cohomology groups of M, with real coefficients, of the partial differential equation theory of generalised Laplacian operators associated to a Riemannian metric on M."
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      "id": "en-Hodge_theory-en-noun-51PC2xYS",
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          "mathematics",
          "mathematics"
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          "differential",
          "differential"
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          "smooth manifold",
          "smooth manifold"
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          "cohomology",
          "cohomology"
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          "group",
          "group"
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          "real",
          "real"
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          "coefficient",
          "coefficient"
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          "partial differential equation",
          "partial differential equation"
        ],
        [
          "Laplacian",
          "Laplacian"
        ],
        [
          "operator",
          "operator"
        ],
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          "Riemannian",
          "Riemannian"
        ],
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          "metric",
          "metric"
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        "(mathematics) One aspect of the study of differential forms of a smooth manifold M. More specifically, it works out the consequences for the cohomology groups of M, with real coefficients, of the partial differential equation theory of generalised Laplacian operators associated to a Riemannian metric on M."
      ],
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        "uncountable"
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        "mathematics",
        "sciences"
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      "wikipedia": [
        "W. V. D. Hodge"
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  ],
  "word": "Hodge theory"
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        "One aspect of the study of differential forms of a smooth manifold M. More specifically, it works out the consequences for the cohomology groups of M, with real coefficients, of the partial differential equation theory of generalised Laplacian operators associated to a Riemannian metric on M."
      ],
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          "mathematics",
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          "smooth manifold",
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          "cohomology",
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          "group",
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          "real",
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          "coefficient",
          "coefficient"
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          "partial differential equation",
          "partial differential equation"
        ],
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          "Laplacian",
          "Laplacian"
        ],
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          "operator",
          "operator"
        ],
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          "Riemannian",
          "Riemannian"
        ],
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          "metric",
          "metric"
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        "(mathematics) One aspect of the study of differential forms of a smooth manifold M. More specifically, it works out the consequences for the cohomology groups of M, with real coefficients, of the partial differential equation theory of generalised Laplacian operators associated to a Riemannian metric on M."
      ],
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