论文标题
具有缺陷的一维拓扑理论：线性案例
One-dimensional topological theories with defects: the linear case
论文作者
论文摘要
本文研究了一个具有缺陷和内部终点的一维拓扑理论的Karoubi包膜，该理论定义在一个领域。事实证明，karoubi信封是由与该理论相关的对称的frobenius代数K决定的。然后，Karoubi信封等于K Modulo的Frobenius-Brauer类别的商，这是可以忽略的态度的理想。对称的Frobenius代数（例如K）描述了薄扁平表面类别的二维TQFT，代数的元素可以变成这些表面侧边界的缺陷。我们还解释了如何将K与限制在封闭表面的通用结构相结合，以定义开放闭合的二维同步性的拓扑理论，该理论通常不是开放式的2D TQFT。
The paper studies the Karoubi envelope of a one-dimensional topological theory with defects and inner endpoints, defined over a field. It turns out that the Karoubi envelope is determined by a symmetric Frobenius algebra K associated to the theory. The Karoubi envelope is then equivalent to the quotient of the Frobenius-Brauer category of K modulo the ideal of negligible morphisms. Symmetric Frobenius algebras, such as K, describe two-dimensional TQFTs for the category of thin flat surfaces, and elements of the algebra can be turned into defects on the side boundaries of these surfaces. We also explain how to couple K to the universal construction restricted to closed surfaces to define a topological theory of open-closed two-dimensional cobordisms which is usually not an open-closed 2D TQFT.
