分层空间、有向Algebraic Topology和状态和TQFT
Stratified spaces, Directed Algebraic Topology, and State-Sum TQFTs
摘要：
我们将Grandis [9，10]发展的有向拓扑理论应用于分层空间的研究，描述了几种方法，其中分层或在分层上具有方向的分层可以用于产生相关的有向空间结构。该描述提供了用于具有缺陷的状态和TQFT的构造的设置[5，8]，我们将其扩展到Dijkgraaf-Witten型TQFT的类似构造，在这种情况下，缺陷（较低维度层）不是源或目标，而是根据取向约定，源在一侧，目标在另一侧。
英文摘要：
We apply the theory of directed topology developed by Grandis [9, 10] to the study of stratified spaces by describing several ways in which a stratification or a stratification with orientations on the strata can be used to produce a related directed space structure. This description provides a setting for the constructions of state-sum TQFTs with defects of [5, 8], which we extend to a similar construction of a Dijkgraaf- Witten type TQFT in the case where the defects (lower dimensional strata) are not sources or targets, but sources on one side and targets on the other, according to an orientation convention.
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