  A new global approach in the study of duality transformations is introduced.
The geometrical structure of complex line bundles is generalized to higher
order U(1) bundles which are classified by quantized charges and duality maps
are formulated over these structures. Quantum equivalence is shown between dual
theories. A global constraint is proven to be needed to achieve well defined
bundles. These global structures are used to refine the proof of the duality
equivalence between d=11 supermembrane and d=10 IIA Dirichlet supermembrane,
giving a complete topological interpretation to their quantized charges.
