Spacetime Topology, Conserved Charges, and the Splitting of Classical Multiplets

We examine consequences of non-trivial topology in background spacetimes and super-spacetimes: It is shown how the semi-invariance of a brane Lagrangian under supertranslations gives rise to topological extensions of the Noether charge algebra carried by D-branes. We investigate how isometry groups of lightlike compactified spacetimes admit an extension to a semigroup. It is shown how the splitting of classical multiplets caused by multiply-connectedness of a phase space can be described in the framework of Symplectic Geometry, based on the concept of symplectic covering spaces and local moment maps.