Cotangent Space - Exterior Powers

Exterior Powers

The k-th exterior power of the cotangent space, denoted Λk(T_x*M), is another important object in differential geometry. Vectors in the kth exterior power, or more precisely sections of the k-th exterior power of the cotangent bundle, are called differential k-forms. They can be thought of as alternating, multilinear maps on k tangent vectors. For this reason, tangent covectors are frequently called one-forms.