The Global Topology of Pontrjagin Duality

Details The Global Topology of Pontrjagin Duality The Global Topology of Pontrjagin Duality

2010-07-26

arxiv.org/abs/1007.4391v2

Mathematics

Operator Algebras

46 pages

Scientific paper

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.

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