The Global Topology of Pontrjagin Duality
Ansgar Schneider

TL;DR
This paper extends Pontrjagin duality within fibre bundle frameworks, defining a Fourier transform via duality triples that generalizes classical group $C^*$-algebra isomorphisms.
Contribution
It introduces a novel fibre bundle-based approach to Pontrjagin duality, establishing a generalized Fourier transform and isomorphism of Hilbert $C^*$-modules.
Findings
Defines a Fourier transform using Pontrjagin duality triples
Establishes an isomorphism of Hilbert $C^*$-modules
Generalizes classical duality between group $C^*$-algebras and functions
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 -modules which generalises the classical isomorphism between the group -algebra of a group and the continuous functions vanishing at infinity on the dual group.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematical Dynamics and Fractals · semigroups and automata theory
