Abstract
The aim of this article is twofold: first, we show how to recover the smooth Deligne-Beilinson cohomology groups from a Heegaard splitting of a closed oriented smooth 3-manifold by extending the usual Čech-de Rham construction; second, thanks to the above and still relying on a Heegaard splitting, we explain how to compute the partition functions of the U(1) Chern-Simons and BF theories.
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