A modular tensor category $\mathcal{C}$ gives rise to a Reshetikhin-Turaev type topological quantum field theory which is defined on 3-dimensional bordisms with embedded $\mathcal{C}$-coloured ribbon graphs. We extend this construction to include bordisms with surface defects which in turn can meet along line defects. The surface defects are labelled by $\Delta$-separable symmetric Frobenius algebras and the line defects by "multi-modules" which are equivariant with respect to a cyclic group action. Our invariant cannot distinguish non-isotopic embeddings of 2-spheres, but we give an example where it distinguishes non-isotopic embeddings of 2-tori.

中文翻译：

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Reshetikhin-Turaev TQFT 中的线和表面缺陷

模张量类别 $\mathcal{C}$ 产生了 Reshetikhin-Turaev 型拓扑量子场论，该理论定义在具有嵌入的 $\mathcal{C}$ 色带图的 3 维 bordisms 上。我们将这种结构扩展到包括具有表面缺陷的 bordisms，这些表面缺陷反过来可以满足沿线缺陷。表面缺陷由 $\Delta$ 可分对称 Frobenius 代数标记，线缺陷由“多模”标记，它们对于循环群作用是等变的。我们的不变量无法区分 2-球体的非同位素嵌入，但我们举了一个例子，它区分了 2-tori 的非同位素嵌入。