  Consider a projective manifold X and suppose that some wedge power of the
cotangent bundle contains a subsheaf whose determinant bundle has maximal
Kodaira dimension. Then we prove that X is of general type. More generally we
compute the Kodaira dimension if the determinant bundle has sufficiently large
Kodaira dimension. This is based on the study of the determinant bundle of a
quotient of the cotangent bundle of a non-uniruled manifold: this bundle is
always pseudo-effective. We apply this to study the universal cover of a
projective manifold. Finally we prove the following: if the canonical bundle is
numerically equivalent to an effective Q-divisor, then the Kodaira dimension is
non-negative.
