三维拓扑模型和heegard分裂。2庞特里亚金对偶和可观测物

F. Thuillier
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引用次数: 0

摘要

在上一篇文章中,给出了用Heegaard分割X_L \cup_f X_R$表示的闭$3$流形$M$上光滑delign - beilinson上同调群$H^p_D(M)$的构造。在此基础上,推导出了$U(1)$ chen - simons和BF量子场论配分函数的确定。在第二篇也是最后一篇文章中,我们将在Heegaard对$M$的描述中定义delign - beilinson $1$-流,其等价类构成$H^1_D(M)^\star$的元素,$H^1_D(M)$的Pontryagin对偶。最后,我们利用奇异场首先恢复了$U(1)$ chen - simons和BF量子场理论的配分函数,然后确定了这些理论定义的链接不变量。讨论了光滑场和奇异场的区别。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
3D topological models and Heegaard splitting. II. Pontryagin duality and observables
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.
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