{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:b536c648-0767-49e9-b712-1849d0825566",
  "labels": {
    "zh-CN": "德拉姆上同调",
    "en": "de Rham cohomology"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "eb9fd4ac99275c559924abd284665ab295bbcdba5df559977c759c7be487d96d",
  "occurrences": [
    {
      "concept_id": "urn:uuid:b536c648-0767-49e9-b712-1849d0825566",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-17/04-homology-and-cohomology",
      "anchor": "first-57c2dbd73bffb785e74e-zh",
      "chapter": "17",
      "section": "17.4",
      "offset": 14784,
      "range": [
        19081,
        19326
      ],
      "source_revision": "962da89618680522177106de9b1899c86eb3dedc9484f12c33659d432388a117",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "德拉姆上同调(de Rham cohomology)",
      "context": {
        "range": [
          19073,
          19796
        ],
        "quote": "第 $r$ 个 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:b536c648-0767-49e9-b712-1849d0825566\" data-concept-route=\"/concept-identities#concept-b536c648-0767-49e9-b712-1849d0825566\" id=\"first-57c2dbd73bffb785e74e-zh\">德拉姆上同调(de Rham cohomology)</u> 空间（群）定义为商空间 $H ^ { r } ( M ) = Z ^ { r } ( M ) / B ^ { r } ( M )$，并且任意两个 $r$ 上闭链 $\\alpha$ 与 $\\beta$ 称为 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:114ca9e4-e0ac-482e-9731-3186bbc7dbfa\" data-concept-route=\"/concept-identities#concept-114ca9e4-e0ac-482e-9731-3186bbc7dbfa\" id=\"first-9f5e2943e091be4de6eb-zh\">上同调的(cohomologous)</u>，如果它们属于同一个陪集，即对某个 $(r-1)$ 上链 $\\gamma$ 有 ${ \\alpha - \\beta = { \\mathrm { d } } \\gamma }$。向量空间 $H ^ { r } ( M )$ 的维数记为 $b ^ { r }$。",
        "quote_sha256": "c9b4094d7d839541cc66220c4b0114acce3f26905611136b643e2cd0eae9f689",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-17/04-homology-and-cohomology",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-3cb8e370c4de42082bfed48a"
    },
    {
      "concept_id": "urn:uuid:b536c648-0767-49e9-b712-1849d0825566",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "en",
      "route": "en/chapter-17/04-homology-and-cohomology",
      "anchor": "first-57c2dbd73bffb785e74e-en",
      "chapter": "17",
      "section": "17.4",
      "offset": 18469,
      "range": [
        22293,
        22530
      ],
      "source_revision": "bcdaffd9c93fa5d4dbb16ac427fef782512ff58c5d5472ea282c7769a2173a3d",
      "source_category": "original_transcription",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "de Rham cohomology",
      "context": {
        "range": [
          22283,
          23122
        ],
        "quote": "The $r$th <u class=\"concept-term\" data-concept-identity=\"urn:uuid:b536c648-0767-49e9-b712-1849d0825566\" data-concept-route=\"/concept-identities#concept-b536c648-0767-49e9-b712-1849d0825566\" id=\"first-57c2dbd73bffb785e74e-en\">de Rham cohomology</u> space (group) is defined as the factor space $H ^ { r } ( M ) = Z ^ { r } ( M ) / B ^ { r } ( M )$ , and any two $r$-cocycles $\\alpha$ and $\\beta$ are said to be <u class=\"concept-term\" data-concept-identity=\"urn:uuid:114ca9e4-e0ac-482e-9731-3186bbc7dbfa\" data-concept-route=\"/concept-identities#concept-114ca9e4-e0ac-482e-9731-3186bbc7dbfa\" id=\"first-9f5e2943e091be4de6eb-en\">cohomologous</u> if they belong to the same coset, ${ \\alpha - \\beta = { \\mathrm { d } } \\gamma }$ for some $(r-1)$-cochain $\\gamma$ . The dimensions of the vector spaces $H ^ { r } ( M )$ are denoted $b ^ { r }$ .",
        "quote_sha256": "a02938e9c1d03099ab1e4b5a2689374d815da97775e2178f041a2730a733af0d",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "zh/chapter-17/04-homology-and-cohomology",
          "lang": "zh-CN",
          "source_category": "translation",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-b43b64d429b25f8c1e6cb264"
    }
  ],
  "registered_positions": [
    {
      "route": "en/chapter-17/04-homology-and-cohomology",
      "lang": "en",
      "section": "17.4",
      "signal": "term-mark",
      "label": "de Rham cohomology",
      "english": "de Rham cohomology",
      "offset": 15066
    },
    {
      "route": "zh/chapter-17/04-homology-and-cohomology",
      "lang": "zh-CN",
      "section": "17.4",
      "signal": "term-mark",
      "label": "德拉姆上同调",
      "english": "de Rham cohomology",
      "offset": 11451
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-3cb8e370c4de42082bfed48a",
    "occ-b43b64d429b25f8c1e6cb264"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 2,
    "located_occurrences": 2,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "b93075e73ba1081bb036b141a8a9dd149b0a52f1da61e3972596db5d4ef95f09",
  "optional_enrichments": []
}