Abstract
We construct a central extension of the smooth Deligne cohomology group of a compact oriented odd dimensional smooth manifold, generalizing that of the loop group of the circle. While the central extension turns out to be trivial for a manifold of dimension 3 , 7 , 11 , … , it is non-trivial for 1 , 5 , 9 , … . In the case where the central extension is non-trivial, we show an analogue of the Segal–Witten reciprocity law.
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