Hodge theory

noun

One aspect of the study of differential forms 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.

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Meanings

nounHodge theory (uncountable)
  1. uncountablemathematicsOne aspect of the study of differential forms 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.

Origin

Named after W. V. D. Hodge.

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Cite this entry
APA

Hodge theory. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Hodge%20theory

MLA

“Hodge theory.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Hodge%20theory. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Hodge theory,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Hodge%20theory.

Source: Hodge theory on Wiktionary, CC BY-SA 4.0.