Poincaré duality
duality that relates homology and cohomology groups for oriented closed manifolds
| rdfs:label |
"Poincaré duality"@en
|
|
skos:alt |
"Poincare duality"@en
|
| schema:description |
"duality that relates homology and cohomology groups for oriented closed manifolds"@en
|
|
schema:date |
"2026-04-02T09:33:58+00:00"^^xsd:dateTime |
| schema:version | 2477388705 |
| wikibase:identifiers | 6 |
| wikibase:sitelinks | 13 |
| wikibase:statements | 21 |
| p:P10283 | wd:statement/Q2063099-C9608EA3-05F4-4D10-90D5-B1ADAC2C0546 |
| p:P138 | wd:statement/Q2063099-275801e4-432c-55bf-200b-de51b59e7b0d |
| p:P1482 | wd:statement/Q2063099-0f8e7ae5-4208-435b-adae-dfa8f4299418 |
| p:P2534 | wd:statement/Q2063099-bd35765b-4712-af1a-3a8e-4b7a48a7e239 |
| p:P2579 | wd:statement/Q2063099-6EC08168-601F-473C-B4ED-3D01AEE29F28 |
| p:P31 | wd:statement/Q2063099-789075d7-4634-9969-a477-9a6b6f33fdab |
| wd:statement/Q2063099-f41cbe59-4636-ce32-60d4-cbd21adfbde5 | |
| p:P361 | wd:statement/Q2063099-D86D7B0F-5C51-4684-B3BD-382B1302310F |
| p:P4215 | wd:statement/Q2063099-4FA05CE3-476F-4C25-B23E-280552B3BBF9 |
| p:P575 | wd:statement/Q2063099-b99cd455-4f56-0e07-8443-2f854a638efe |
| p:P61 | wd:statement/Q2063099-28bcddbe-4bd0-270d-fc85-308d723a0c34 |
| p:P6104 | wd:statement/Q2063099-11B6B4F8-C50A-496F-B290-592851BFFFAA |
| p:P6366 | wd:statement/Q2063099-E82AA6E5-D43E-4585-8910-28A893293F08 |
| p:P646 | wd:statement/Q2063099-F2D03A6D-4BAB-424A-824C-C2A8E1BB6A48 |
| p:P7235 | wd:statement/Q2063099-06b3eab3-46e6-16e0-f1dd-4c55eca436df |
| wd:statement/Q2063099-6526d40e-4cb5-8955-d5c4-d90275834345 | |
| wd:statement/Q2063099-655d1a8a-45f5-1252-0b2d-274bfff88a84 | |
| wd:statement/Q2063099-6b9424d9-436e-2ee0-7aec-7cbdbed9ed12 | |
| wd:statement/Q2063099-98d6e58e-4dcd-9e3f-7bda-7f631284a5ce | |
| p:P7554 | wd:statement/Q2063099-0bce00c2-4899-2e37-ad85-bf08cbb1ccf5 |
| p:P7726 | wd:statement/Q2063099-e499285d-4454-8fec-7a9f-109e51facf85 |
|
p:direct- |
<https:/ |
| wdt:P10283 | "C26390989" |
| wdt:P138 | Henri Poincaré |
| wdt:P1482 |
<https:/ |
| 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>α</mi></mtd><mtd><mo stretchy="false">↦</mo><mo stretchy="false">[</mo><mi>M</mi><mo stretchy="false">]</mo><mo stretchy="false">⌢</mo><mi>α</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">→</mo></mrow><mo stretchy="false">≅</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>⁡</mo><mo stretchy="false">(</mo><mi>M</mi><mo stretchy="false">)</mo><mo stretchy="false">−</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 | homology theory |
| wdt:P31 | duality |
| theorem | |
| wdt:P361 | list of theorems |
| wdt:P4215 | "Poincaré duality" |
| wdt:P575 | "1893-01-01T00:00:00+00:00"^^xsd:dateTime |
| wdt:P61 | Henri Poincaré |
| wdt:P6104 | WikiProject Mathematics |
| 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>⁡</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">⌢</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" |
Download as: