论文标题
基于3组的4个manifolds的拓扑不变
Topological invariant of 4-manifolds based on a 3-group
论文作者
论文摘要
我们研究了较高仪表理论的背景下4维BF理论的概括。我们基于经典3BF动作的一般3组和4维时空歧管构建三角构造的独立拓扑状态总和Z。该状态总和与Porter的TQFT重合d = 4和n = 3。为了验证构建的状态总和是基础4维流形的拓扑不变，分析了其在Pachner移动下的行为，并且可以获得状态总和Z保持不变。本文是对Girelli，Pfeiffer和Popescu所做的工作的概括，以基于经典的2BF动作和基础的2组结构进行状态总和。
We study a generalization of a 4-dimensional BF-theory in the context of higher gauge theory. We construct a triangulation independent topological state sum Z, based on the classical 3BF action for a general 3-group and a 4-dimensional spacetime manifold. This state sum coincides with Porter's TQFT for d=4 and n=3. In order to verify that the constructed state sum is a topological invariant of the underlying 4-dimensional manifold, its behavior under Pachner moves is analyzed, and it is obtained that the state sum Z remains the same. This paper is a generalization of the work done by Girelli, Pfeiffer, and Popescu for the case of state sum based on the classical 2BF action with the underlying 2-group structure.
