3D topological models and Heegaard splitting. II. Pontryagin duality and observables

Abstract

In a previous article, a construction of the smooth Deligne-Beilinson cohomology groups H p D (M) on a closed 3-manifold M represented by a Heegaard splitting X L ∪ f X R was presented. Then, a determination of the partition functions of the U(1) Chern-Simons and BF Quantum Field theories was deduced from this construction. In this second and concluding article we stay in the context of a Heegaard spitting of M to define Deligne-Beilinson 1-currents whose equivalent classes form the elements of H 1 D (M) ⋆ , the Pontryagin dual of H 1 D (M). Finally, we use singular fields to first recover the partition functions of the U(1) Chern-Simons and BF quantum field theories, and next to determine the link invariants defined by these theories. The difference between the use of smooth and singular fields is also discussed.