We develop a graphical calculus of manifold diagrams which generalises string and surface diagrams to arbitrary dimensions. Manifold diagrams are pasting diagrams for $(\infty, n)$-categories that admit a semi-strict composition operation for which associativity and unitality is strict. The weak interchange law satisfied by composition of manifold diagrams is determined geometrically through isotopies of diagrams. By building upon framed combinatorial topology, we can classify critical points in isotopies at which the arrangement of cells changes. This allows us to represent manifold diagrams combinatorially and use them as shapes with which to probe $(\infty, n)$-categories, presented as $n$-fold Segal spaces. Moreover, for any system of labels for the singularities in a manifold diagram, we show how to generate a free $(\infty, n)$-category.

翻译：我们发展了一套流形图的图形演算，将弦图和曲面图推广至任意维度。流形图是$(\infty, n)$-范畴的粘贴图，允许具有严格结合律与单位元的半严格合成运算。流形图合成所满足的弱交换律通过图的同痕几何地确定。基于框架组合拓扑学，我们能够对同痕中胞腔排布发生变化的临界点进行分类。这使得我们能够以组合方式表示流形图，并将其用作探测以$n$重Segal空间呈现的$(\infty, n)$-范畴的几何形状。此外，对于流形图中奇点的任意标注系统，我们展示了如何生成自由的$(\infty, n)$-范畴。