Milnor–Wood inequality

The Milnor–Wood inequality is a result in differential geometry and topology that relates to the study of compact manifolds and especially to the theory of bundles over these manifolds. It provides a constraint on the ranks of vector bundles over a manifold in terms of the geometry of the manifold itself. Specifically, the Milnor–Wood inequality offers a bound on the rank of a vector bundle over a compact surface in relation to the Euler characteristic of the surface.