  Pontrjagin duality is implemented in the framework of fibre bundles. By means
of Pontrjagin duality triples a Fourier transform is defined by a pull-push
construction operating on sections of line bundles. This yields an isomorphism
of Hilbert $C^*$-modules which generalises the classical isomorphism between
the group $C^*$-algebra of a group and the continuous functions vanishing at
infinity on the dual group.
