论文标题
图形和广义轨迹的道具
ProPs of graphs and generalised traces
论文作者
论文摘要
我们将广义的卷积（分别痕迹）分配给其边缘在封闭的歧管上被光滑内核（分别平滑算子）装饰的图。为此，我们介绍了陷阱（痕迹和排列）的概念，该概念与不垂直串联的道具（产品和排列）大致相对应，并配备了广义部分痕迹的家族。它们可以配备一种道具结构，从而从部分痕迹得出垂直串联时，我们将陷阱与默克洛夫首先引入的轮子道具相关联。我们进一步构建了它们的自由对象，并提供了道具和陷阱的通用性能的精确证明。
We assign generalised convolutions (resp. traces) to graphs whose edges are decorated by smooth kernels (resp. smoothing operators) on a closed manifold. To do so, we introduce the concept of TraPs (Traces and Permutations), which roughly correspond to ProPs (Products and Permutations) without vertical concatenation and equipped with families of generalised partial traces. They can be equipped with a ProP structure in deriving vertical concatenation from the partial traces and we relate TraPs to wheeled ProPs first introduced by Merkulov. We further build their free object and give precise proofs of universal properties of ProPs and TraPs.
