Duality for topological abelian group stacks and <var>T</var>-duality

  • Ulrich Bunke

    Universität Regensburg, Germany
  • Thomas Schick

    Georg-August-Universität Göttingen, Germany
  • Markus Spitzweck

    Georg-August-Universität Göttingen, Germany
  • Andreas Thom

    Technische Universität Dresden, Germany
Duality for topological abelian group stacks and <var>T</var>-duality cover
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We extend Pontrjagin duality from topological abelian groups to certain locally compact group stacks. To this end we develop a sheaf theory on the big site of topological spaces S in order to prove that the sheaves ExtiShAbS(G,T), i = 1, 2, vanish, where G is the sheaf represented by a locally compact abelian group and T is the circle. As an application of the theory we interpret topological T-duality of principal Tn-bundles in terms of Pontrjagin duality of abelian group stacks.