Hodge theory
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Hodge theory

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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. It was developed by W. V. D. Hodge in the 1930s as an extension of de Rham cohomology, and has major applications on three levels: Riemannian manifolds, Kähler manifolds, algebraic geometry of complex projective varieties, and even more bro...