Poincaré duality
duality that relates homology and cohomology groups for oriented closed manifolds
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Poincaré duality
Summary
Poincaré duality is a theorem[1]. It draws 158 Wikipedia views per month (theorem category, ranking #153 of 1,306).[2]
Key Facts
- Poincaré duality is credited with the discovery of Henri Poincaré[3].
- Poincaré duality's instance of is recorded as theorem[4].
- Poincaré duality's instance of is recorded as duality[5].
- Henri Poincaré is named after Poincaré duality[6].
- Poincaré duality's part of is recorded as list of theorems[7].
- Poincaré duality's time of discovery or invention is recorded as +1893-00-00T00:00:00Z[8].
- Poincaré duality's Freebase ID is recorded as /m/02n4h4[9].
- Poincaré duality's Stack Exchange tag is recorded as https://mathoverflow.net/tags/poincare-duality[10].
- Poincaré duality's defining formula is recorded as \begin{aligned}\alpha&\mapsto[M]\frown\alpha\\operatorname H^k(M)&\overset\cong\to\operatorname H_{\dim(M)-k}(M)\end{aligned}[11].
- Poincaré duality's studied by is recorded as homology theory[12].
- Poincaré duality's nLab ID is recorded as Poincaré duality[13].
- Poincaré duality's maintained by WikiProject is recorded as WikiProject Mathematics[14].
- Poincaré duality's Microsoft Academic ID is recorded as 26390989[15].
- Poincaré duality's in defining formula is recorded as \operatorname H^k(M)[16].
- Poincaré duality's in defining formula is recorded as \operatorname H_k(M)[17].
- Poincaré duality's in defining formula is recorded as [M][18].
- Poincaré duality's in defining formula is recorded as \frown[19].
- Poincaré duality's in defining formula is recorded as \dim(M)[20].
- Poincaré duality's Encyclopedia of Mathematics article ID is recorded as Poincaré_duality[21].
- Poincaré duality's PlanetMath ID is recorded as PoincareDuality[22].
- Poincaré duality's OpenAlex ID is recorded as C26390989[23].
Body
Works and Contributions
Poincaré duality is credited with the discovery of Henri Poincaré[3].
Why It Matters
Poincaré duality draws 158 Wikipedia views per month (theorem category, ranking #153 of 1,306).[2] It has Wikipedia articles in 13 language editions, a strong signal of global cultural recognition.[24] It is known by 5 alternative names across languages and contexts.[25]