@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:Q2063099 rdfs:label "Dualitat de Poincaré"@ca,
        "Poincaré-Dualität"@de,
        "Poincaré-Dualität"@de-ch,
        "Poincaré duality"@en,
        "Poincaré duality"@en-ca,
        "Poincaré duality"@en-gb,
        "dualeco de Poincaré"@eo,
        "dualidad de Poincaré"@es,
        "dualité de Poincaré"@fr,
        "דואליות פואנקרה"@he,
        "ポアンカレ双対"@ja,
        "푸앵카레 쌍대성"@ko,
        "Poincaré-dualiteit"@nl,
        "dualidade de Poincaré"@pt,
        "dualidade de Poincaré"@pt-br,
        "dualitate Poincaré"@ro,
        "двойственность Пуанкаре"@ru,
        "Poincaréjeva dualnost"@sl,
        "Poincarés dualitet"@sv,
        "ภาวะคู่กันปวงกาเร"@th,
        "двоїстість Пуанкаре"@uk,
        "龐加萊對偶性"@zh,
        "庞加莱对偶性"@zh-hans,
        "龐加萊對偶性"@zh-hant ;
    schema1:dateModified "2026-04-02T09:33:58+00:00"^^xsd:dateTime ;
    schema1:description "mathematischer Satz"@de,
        "duality that relates homology and cohomology groups for oriented closed manifolds"@en,
        "dualeco inter la homologio-grupoj kaj la kohomologio-grupoj de orientita fermita sternaĵo"@eo,
        "théorème de mathématiques"@fr,
        "dualnost, ki povezuje homologne in kohomologne grupe za usmerjene zaprte mnogoterosti"@sl ;
    schema1:version 2477388705 ;
    wikibase:identifiers 6 ;
    wikibase:sitelinks 13 ;
    wikibase:statements 21 ;
    skos:altLabel "Poincarédualität"@de,
        "Poincare duality"@en,
        "Poincaré-dualeco"@eo,
        "pojnkara dualeco"@eo,
        "dualidad de Poincare"@es,
        "ポアンカレ双対性"@ja,
        "Poincare-dualiteit"@nl ;
    p:P10283 wds:Q2063099-C9608EA3-05F4-4D10-90D5-B1ADAC2C0546 ;
    p:P138 wds:Q2063099-275801e4-432c-55bf-200b-de51b59e7b0d ;
    p:P1482 wds:Q2063099-0f8e7ae5-4208-435b-adae-dfa8f4299418 ;
    p:P2534 wds:Q2063099-bd35765b-4712-af1a-3a8e-4b7a48a7e239 ;
    p:P2579 wds:Q2063099-6EC08168-601F-473C-B4ED-3D01AEE29F28 ;
    p:P31 wds:Q2063099-789075d7-4634-9969-a477-9a6b6f33fdab,
        wds:Q2063099-f41cbe59-4636-ce32-60d4-cbd21adfbde5 ;
    p:P361 wds:Q2063099-D86D7B0F-5C51-4684-B3BD-382B1302310F ;
    p:P4215 wds:Q2063099-4FA05CE3-476F-4C25-B23E-280552B3BBF9 ;
    p:P575 wds:Q2063099-b99cd455-4f56-0e07-8443-2f854a638efe ;
    p:P61 wds:Q2063099-28bcddbe-4bd0-270d-fc85-308d723a0c34 ;
    p:P6104 wds:Q2063099-11B6B4F8-C50A-496F-B290-592851BFFFAA ;
    p:P6366 wds:Q2063099-E82AA6E5-D43E-4585-8910-28A893293F08 ;
    p:P646 wds:Q2063099-F2D03A6D-4BAB-424A-824C-C2A8E1BB6A48 ;
    p:P7235 wds:Q2063099-06b3eab3-46e6-16e0-f1dd-4c55eca436df,
        wds:Q2063099-6526d40e-4cb5-8955-d5c4-d90275834345,
        wds:Q2063099-655d1a8a-45f5-1252-0b2d-274bfff88a84,
        wds:Q2063099-6b9424d9-436e-2ee0-7aec-7cbdbed9ed12,
        wds:Q2063099-98d6e58e-4dcd-9e3f-7bda-7f631284a5ce ;
    p:P7554 wds:Q2063099-0bce00c2-4899-2e37-ad85-bf08cbb1ccf5 ;
    p:P7726 wds:Q2063099-e499285d-4454-8fec-7a9f-109e51facf85 ;
    wdtn:P6366 <https://makg.org/entity/26390989> ;
    wdt:P10283 "C26390989" ;
    wdt:P138 wd:Q81082 ;
    wdt:P1482 <https://mathoverflow.net/tags/poincare-duality> ;
    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\"><mrow data-mjx-texclass=\"ORD\"><mtable columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" displaystyle=\"true\" rowspacing=\"3pt\"><mtr><mtd><mi>&#x03B1;</mi></mtd><mtd><mo stretchy=\"false\">&#x21A6;</mo><mo stretchy=\"false\">[</mo><mi>M</mi><mo stretchy=\"false\">]</mo><mo stretchy=\"false\">&#x2322;</mo><mi>&#x03B1;</mi></mtd></mtr><mtr><mtd><msup><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">H</mi><mrow data-mjx-texclass=\"ORD\"><mi>k</mi></mrow></msup><mo stretchy=\"false\">(</mo><mi>M</mi><mo stretchy=\"false\">)</mo></mtd><mtd><mrow data-mjx-texclass=\"ORD\"><mover><mrow><mo stretchy=\"false\" accent=\"false\">&#x2192;</mo></mrow><mo stretchy=\"false\">&#x2245;</mo></mover></mrow><msub><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">H</mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>dim</mi><mo>&#x2061;</mo><mo stretchy=\"false\">(</mo><mi>M</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">&#x2212;</mo><mi>k</mi></mrow></mrow></msub><mo stretchy=\"false\">(</mo><mi>M</mi><mo stretchy=\"false\">)</mo></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML> ;
    wdt:P2579 wd:Q1626229 ;
    wdt:P31 wd:Q1755512,
        wd:Q65943 ;
    wdt:P361 wd:Q944443 ;
    wdt:P4215 "Poincaré duality" ;
    wdt:P575 "1893-01-01T00:00:00+00:00"^^xsd:dateTime ;
    wdt:P61 wd:Q81082 ;
    wdt:P6104 wd:Q8487137 ;
    wdt:P6366 "26390989" ;
    wdt:P646 "/m/02n4h4" ;
    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>dim</mi><mo>&#x2061;</mo><mo stretchy=\"false\">(</mo><mi>M</mi><mo stretchy=\"false\">)</mo></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\">&#x2322;</mo></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><mi>M</mi><mo stretchy=\"false\">]</mo></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\"><msub><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">H</mi><mrow data-mjx-texclass=\"ORD\"><mi>k</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>M</mi><mo stretchy=\"false\">)</mo></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\"><mi>k</mi></mrow></msup><mo stretchy=\"false\">(</mo><mi>M</mi><mo stretchy=\"false\">)</mo></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML> ;
    wdt:P7554 "Poincaré_duality" ;
    wdt:P7726 "PoincareDuality" .