@prefix p: <http://www.wikidata.org/prop/> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix schema1: <http://schema.org/> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix wd: <http://www.wikidata.org/entity/> .
@prefix wds: <http://www.wikidata.org/entity/statement/> .
@prefix wdt: <http://www.wikidata.org/prop/direct/> .
@prefix wdtn: <http://www.wikidata.org/prop/direct-normalized/> .
@prefix wikibase: <http://wikiba.se/ontology#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

wd:Q40007 rdfs:label "classe de Pontriaguin"@ca,
        "Pontrjagin-Klasse"@de,
        "Pontryagin class"@en,
        "klaso de Pontrjagin"@eo,
        "clase de Pontryagin"@es,
        "classe de Pontriaguine"@fr,
        "ポントリャーギン類"@ja,
        "폰트랴긴 특성류"@ko,
        "klassi ta' Pontrjagin"@mt,
        "classe de Pontryagin"@pt,
        "classe de Pontryagin"@pt-br,
        "класс Понтрягина"@ru,
        "Pontryaginklass"@sv,
        "клас Понтрягіна"@uk,
        "庞特里亚金类"@zh,
        "庞特里亚金类"@zh-hans,
        "龐特里亞金類"@zh-hant ;
    schema1:dateModified "2026-08-27T13:23:54+00:00"^^xsd:dateTime ;
    schema1:description "characteristic class for real vector bundles, whose degree is a multiple of four"@en,
        "karakteriza klaso de reela vektora fasko, kiu estas kohomologia klaso, kies grado estas oblo de kvar"@eo,
        "classes caractéristiques associées aux fibrés vectoriels réels, qui appartiennent aux groupes de cohomologie de degré un multiple de quatre"@fr,
        "4の倍数の次数を持つコホモロジー群の中にある特性類"@ja,
        "klassi karatteristika definita għal gruppi ta' vetturi reali"@mt ;
    schema1:version 2537074426 ;
    wikibase:identifiers 4 ;
    wikibase:sitelinks 9 ;
    wikibase:statements 18 ;
    skos:altLabel "Pontrjagin-a klaso"@eo,
        "klaso de Pontryagin"@eo,
        "pontrjagina klaso"@eo,
        "폰트랴긴 모임"@ko,
        "폰트랴긴류"@ko,
        "Теорема Новикова"@ru ;
    p:P138 wds:Q40007-33df4d4b-4b9f-febb-0243-0386833da4e9 ;
    p:P2534 wds:Q40007-1c104a1c-43c3-dbd1-2c4f-60ad5659130b ;
    p:P279 wds:Q40007-7c5abca3-4f7b-dce7-eda3-34ef562cf372 ;
    p:P2812 wds:Q40007-BDEA5EB2-20A9-4669-908E-ABC62E7F1E26 ;
    p:P31 wds:Q40007-f067ad46-417e-ff7c-f748-1994b26463e7 ;
    p:P4215 wds:Q40007-9ACFBF1D-2236-4807-B10E-A7C968178C0B ;
    p:P61 wds:Q40007-7338bce4-42c1-b28b-5d61-4f35ae776631 ;
    p:P6104 wds:Q40007-1A786BAA-5E65-4E47-8C47-EC7E932DFD11 ;
    p:P6366 wds:Q40007-6F546639-2AE2-4289-9CC8-6B0A920C9504 ;
    p:P646 wds:Q40007-BD51CEE8-E98E-47D2-9D52-0A24C08D29BB ;
    p:P7235 wds:Q40007-10320d40-401a-1a75-d981-bded87beca92,
        wds:Q40007-322ff737-4c56-47f0-08fd-f23848fe1afd,
        wds:Q40007-62fcf2dc-490d-c410-f015-68537b86a290,
        wds:Q40007-90c9793a-42a0-25e5-ccdf-95b39eabc593,
        wds:Q40007-a0b34c75-4cdb-24f7-8fc1-e97b6884c0a1,
        wds:Q40007-a603922f-413e-cdf8-4998-4edc4e5779c0,
        wds:Q40007-b78f2f95-45c6-f5d2-84cb-57fca261a467,
        wds:Q40007-ff008bc1-4552-0930-d028-f47e83a2fafb ;
    wdtn:P6366 <https://makg.org/entity/156840345> ;
    wdt:P138 wd:Q451319 ;
    wdt:P2534 "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><msub><mi>p</mi><mrow data-mjx-texclass=\"ORD\"><mi>k</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>E</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">=</mo><mo stretchy=\"false\">(</mo><mo stretchy=\"false\">−</mo><mn>1</mn><msup><mo stretchy=\"false\">)</mo><mrow data-mjx-texclass=\"ORD\"><mi>k</mi></mrow></msup><msub><mi>c</mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn>2</mn><mi>k</mi></mrow></mrow></msub><mo stretchy=\"false\">(</mo><mi>E</mi><mo stretchy=\"false\">⊗</mo><mrow data-mjx-texclass=\"ORD\"><mi>ℂ</mi></mrow><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">∈</mo><msup><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">H</mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn>4</mn><mi>k</mi></mrow></mrow></msup><mo stretchy=\"false\">(</mo><mi>M</mi><mo stretchy=\"false\">)</mo></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML> ;
    wdt:P279 wd:Q1062978 ;
    wdt:P2812 "PontryaginClass" ;
    wdt:P31 wd:Q24034552 ;
    wdt:P4215 "Pontryagin class" ;
    wdt:P61 wd:Q451319 ;
    wdt:P6104 wd:Q8487137 ;
    wdt:P6366 "156840345" ;
    wdt:P646 "/m/0225nj" ;
    wdt:P7235 "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mi>E</mi></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML>,
        "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mi>M</mi></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML>,
        "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mi>c</mi></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML>,
        "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mi>k</mi></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML>,
        "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mi>p</mi></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML>,
        "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mo stretchy=\"false\">−</mo><mn>1</mn></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML>,
        "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mo stretchy=\"false\">⊗</mo><mrow data-mjx-texclass=\"ORD\"><mi>ℂ</mi></mrow></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML>,
        "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><msup><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">H</mi><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">∙</mo></mrow></msup></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML> .

