Hodge's Theorem

On a compact oriented Finsler Manifold without boundary, every Cohomology class has a Unique harmonic representative. The Dimension of the Space of all harmonic forms of degree $p$ is the $p$th Betti Number of the Manifold.

See also Betti Number, Cohomology, Dimension, Finsler Manifold

References

Chern, S.-S. ``Finsler Geometry is Just Riemannian Geometry without the Quadratic Restriction.'' Not. Amer. Math. Soc. 43, 959-963, 1996.