e/Hodge theory

Information
has gloss	eng: In mathematics, Hodge theory, named after W. V. D. Hodge, is one aspect of the study of the algebraic topology of a smooth manifold M. More specifically, it works out the consequences for the cohomology groups of M, with real coefficients, of the partial differential equation theory of generalised Laplacian operators associated to a Riemannian metric on M.
lexicalization	eng: Hodge theory
instance of	e/Complex manifold

Meaning
Dutch
has gloss	nld: In de wiskunde is de Hodge-theorie, vernoemd naar W.V.D. Hodge, een aspect van de bestudering van de algebraïsche topologie van een gladde variëteit M. Meer in het bijzonder houdt de Hodge-theorie zich bezig met de gevolgen voor de cohomologiegroepen van M (met reële coëfficiënten) van de partiële differentiaalvergelijkingtheorie van veralgemeende Laplaciaanse operatoren geassocieerd met een Riemann-metriek op M.
lexicalization	nld: Hodge-theorie
Portuguese
has gloss	por: Em matemática, teoria de Hodge, nomeada em referência a W. V. D. Hodge, é um aspecto do estudo da topologia algébrica de uma variedade diferenciável M. Mais especificamente, funciona com as consequências das cohomologias de grupos de M, com coeficientes reais, da teoria da equação diferencial parcial de operadores Laplacianos generalizados associados a uma métrica Riemanniana sobre M.
lexicalization	por: Teoria de Hodge
Chinese
has gloss	zho: 数学上，霍奇理论是光滑流形M的代数拓扑的研究的一个方面。更精确的讲，它寻找M的实系数上同调群在和M上的黎曼度量相关的一般化的拉普拉斯算子的偏微分方程理论中的应用。
lexicalization	zho: 霍奇理论