The two expressions are derived from identities involving the cotangent and cosecant functions. See also tangent bundle and cotangent bundle. Floer homology by and for the symplectic Floer homology of cotangent bundles by Cohen. Here, the canonical bundle is the same as the (holomorphic) cotangent bundle. The total space of a cotangent bundle has the structure of a symplectic manifold. In symplectic geometry one is instead interested in exterior powers of the cotangent bundle. The elements of the cotangent space are called cotangent vectors or tangent covectors. The Hamiltonian is a scalar on the cotangent bundle. In general, an "n"-form is a tensor with cotangent rank "n" and tangent rank 0. Concretely, elements of the cotangent space are linear functionals on "formula 6". This construction is in particular applied to the cotangent bundle of a smooth manifold. Smooth sections of the cotangent bundle are called (differential) one-forms. It can be realised naturally as a sub-bundle of the cotangent bundle. Likewise, a 1-form on formula 28 is a section of the cotangent bundle. The elements of formula 4 are called cotangent vectors.