Atiyah-Singer index theorem in English

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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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        "Atiyah-Singer index theorem"
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  "word": "Atiyah-Singer index theorem"
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[Show JSON for raw wiktextract data ▼] [Hide JSON for raw wiktextract data ▲]

{
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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)."
      ],
      "links": [
        [
          "differential geometry",
          "differential geometry"
        ],
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          "elliptic differential operator",
          "elliptic operator"
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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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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

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"Atiyah-Singer index theorem" meaning in English

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