论文标题
树木，图形和骨料：组合表面拓扑，几何学和代数的分类视角
Trees, graphs and aggregates: a categorical perspective on combinatorial surface topology, geometry, and algebra
论文作者
论文摘要
从Feynman的分类角度来看，表面几何形状的几个关键方面是从与图的组合结构中推导的。这提供了从图形组合到通过拓扑，几何和代数的字符串拓扑操作的直接途径。 特别是，将树包含在图中，并且将图形分解为聚集体产生了一种简洁的形式主义，用于循环和模块化过程，以及它们的多环和表面类型的概括。后者在二维拓扑场理论和弦拓扑中显着发生。分类观点使我们可以将Feynman操作的左KAN扩展作为有效的计算工具。这些计算涉及对某些类别的结构化图的研究，这些图被预期具有独立感兴趣。
Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route from combinatorics of graphs to string topology operations via topology, geometry and algebra. In particular, the inclusion of trees into graphs and the dissection of graphs into aggregates yield a concise formalism for cyclic and modular operads as well as their polycyclic and surface type generalizations. The latter occur prominently in two-dimensional topological field theory and in string topology. The categorical viewpoint allows us to use left Kan extensions of Feynman operations as an efficient computational tool. The computations involve the study of certain categories of structured graphs which are expected to be of independent interest.
