In his PhD thesis [G. Goosen, Oriented 123-tqfts via string-nets and state-sums, PhD thesis, Stellenbosch University, Stellenbosch (2018)], Goosen combined the string-net and the generators-and-relations formalisms for arbitrary once-extended 3-dimensional topological quantum field theories (TQFTs). In this paper, we work this out in detail for the simplest nontrivial example, where the underlying spherical fusion category is the category of ℤ/2ℤ-graded vector spaces. This allows us to give an elementary string-net description of the linear maps associated to 3-dimensional bordisms. The string-net formalism also simplifies the description of the mapping class group action in the resulting TQFT. We conclude the paper by performing some example calculations from this viewpoint.

中文翻译：

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通过生成器和关系的扩展 TQFT I：扩展的复曲面代码

在他的博士论文中 [G. Goosen, Oriented 123-tqfts via string-nets and state-sums, 博士论文, Stellenbosch University, Stellenbosch (2018)], Goosen 将弦网和生成器和关系形式结合起来用于任意一次扩展的 3 维拓扑量子场论（TQFT）。在本文中，我们针对最简单的非平凡示例详细解决了这一问题，其中基础球面融合类别是ℤ/2ℤ分级向量空间。这使我们能够给出与 3 维边界相关的线性映射的基本弦网描述。串网形式也简化了生成的 TQFT 中映射类组动作的描述。我们通过从这个角度执行一些示例计算来结束本文。