The Global Topology of Pontrjagin Duality

Abstract

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 $C^{\ast }$-modules which generalises the classical isomorphism between the group $C^{\ast }$-algebra of a group and the continuous functions vanishing at infinity on the dual group.

46 pages

References in corpus (2)

• Introduction to the language of stacks and gerbes
• Die lokale Struktur von T-Dualitätstripeln