monojussi:
Taking wedge products of these harmonic representatives corresponds to the cup product in cohomology, so the cup product is compatible with the Hodge decomposition
monojussi:
Assume X is a Kähler manifold, so that there is a decomposition on its cohomology with complex coefficients
monojussi:
Then X is an orientable smooth manifold of real dimension 2n, so its cohomology groups lie in degrees zero through 2n.
monojussi:
Let X be a compact complex manifold of complex dimension n
monojussi:
Riemann hypothesis
monojussi:
Yang–Mills existence and mass gap