论文标题
3D拓扑模型和Heegaard拆分II：Pontryagin二元性和可观察力
3D Topological Models and Heegaard Splitting II: Pontryagin duality and Observables
论文作者
论文摘要
在上一篇文章中，在封闭的$ 3 $ -MANIFOLD $ M $上构建了Smooth Deligne-Beilinson共同学组$ h^p_d（m）$，以Heegaard分配为$ x_l \ cup_f x_r $表示。然后，确定了$ u（1）$ chern-simons和bf量子场理论的分区功能的确定。在第二篇和结论的文章中，我们始终以$ m $的heegaard吐痰来定义deligne-beilinson $ 1 $ currents，其等效类形成$ h^1_d（m）^\ star $的元素，pontryagin Dual of $ h^1_d（m）$。最后，我们使用单数字段首先恢复$ u（1）$ chern-simons和bf量子字段理论的分区功能，然后确定这些理论定义的链接不变性。还讨论了平滑和奇异场的使用之间的差异。
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 $X_L \cup_f X_R$ 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 $H^1_D(M)^\star$, 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.
