Hodge theory
= Hodge theory
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Hodge theory connects <de Rham cohomology> with <harmonic differential forms> through the <Hodge Laplacian> on a compact <Riemannian manifold>. The <Hodge decomposition theorem> supplies a unique harmonic representative of each cohomology class. On a compact <Kähler manifold>, the decomposition additionally respects the complex bidegrees of <differential forms>.