论文标题
组合恢复理论
Combinatorial Cobordism Theory
论文作者
论文摘要
我们引入了一种基于细胞复杂组合概念的形式主义，视包含在包含的二元性操作中。我们的主要目标是在不假定多种形式或拓扑结构的上下文中为现场理论的函数定义打开道路。这是通过定义组成操作的离散概念来实现的。我们的主要定理通过表明细胞复合物之间的某些地图序列与较高的尺寸的细胞络合物相对应，从而实现了恢复的组成。结果，我们获得了一个类别，其形态是具有因果结构的共生性，该因果结构概括了因果动力学三角剖分以及从细胞复合物定义的二元性图遗传的二元性。
We introduce a formalism based on a combinatorial notion of cell complex subject to an inclusion-reversing duality operation. Our main goal is to open the way for a functorial definition of field theories in a context where no manifold or topological structure is assumed. This is achieved via a discrete notion of cobordism for which a composition operation is defined. Our main theorem enables the composition of cobordisms by showing that certain sequences of maps between cell complexes are in bijective correspondence with a cell complex of dimension one higher. As a result we obtain a category whose morphisms are cobordisms having a causal structure generalizing that of Causal Dynamical Triangulations as well as dualities inherited from the duality map defined on cell complexes.
