Some parameterizations are easier to work with than others, and many important statements can be made by working in a coordinate-free fashion. Examples of coordinate-free statements are that the tangent space T Q corresponds to the velocities of the points q ∈ ∈ Q , while the cotangent space T ∗ ∗ Q corresponds to momenta. (Velocities and momenta can be connected; for the most general, abstract case, this is done with the rather abstract notion of the tautological one-form.)