论文标题
通过发电机和关系I：扩展的tQfts扩展的TQFT：扩展的复曲面代码
Extended TQFTs via Generators and Relations I: The Extended Toric Code
论文作者
论文摘要
在他的博士学位论文中，GOOSEN结合了字符串网络以及一度延伸的3维TQFT的形式和形式主义。在本文中，我们详细介绍了最简单的非平凡示例，其中基础球形融合类别是$ \ mathbb {z}/2 \ mathbb {z} $ - 分级向量空间的类别。这使我们可以给出与3维伴侣关联的线性图的基本字符串网络描述。字符串 - 网格形式主义还简化了所得TQFT中映射类组动作的描述。我们通过从此角度执行一些示例计算来结束论文。
In his PhD thesis, Goosen combined the string-net and the generators-and-relations formalisms for arbitrary once-extended 3-dimensional TQFTs. In this paper we work this out in detail for the simplest non-trivial example, where the underlying spherical fusion category is the category of $\mathbb{Z}/2\mathbb{Z}$-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.
