The classification of differential structures on quantum 2-spheres

Exterior algebras of differential forms on quantum 2-spheres Sqc2, qelement of[-1, 1]inverse slant{0}, element of[0, ∞] (c=0 for q=±1), are classified. In the definition of exterior algebras we assume the invariance w.r.t. the action of the quantum SU(2) group and 'dimensionality conditions' (which imply that we deal with 'two-dimensional manifolds'). The exterior algebras exist only for c=0 and are unique in that case. The corresponding generalized directional derivatives are provided. (orig.)