论文标题
通过弦网和二维手术的三维TQFTS
Three-dimensional TQFTs via string-nets and two-dimensional surgery
论文作者
论文摘要
如果$ c $是球形融合类别，则将弦网构造与每个定向封闭的表面$σ$ vector Space $ z_ \ z_ \ text {sn}（σ）$ $ c $ c $ labellabelled图形的线性组合的$ c $ c $ c $ c $ co $σ$ modulo local关系的$，在某种程度上与方面的差异相比，在某种程度上是在方面的差异。我们通过确定Juhász中的手术发生器如何在弦 - 网络矢量空间上对Juhász的呈现方式来确定如何将此分配扩展到三维拓扑量子场理论（TQFT）。我们表明，所得的TQFT是用字符串网络的二维图形语言制定的，它是Turaev-Viro state Sum模型的替代描述。
If $C$ is a spherical fusion category, the string-net construction associates to each closed oriented surface $Σ$ the vector space $Z_\text{SN}(Σ)$ of linear combinations of $C$-labelled graphs on $Σ$ modulo local relations, in a way which is functorial with respect to orientation-preserving diffeomorphisms of surfaces. We show how to extend this assignment to a 3-dimensional topological quantum field theory (TQFT), by defining how the surgery generators in Juhász' presentation of the oriented 3-dimensional bordism category act on the string-net vector spaces. We show that the resulting TQFT, which is formulated completely in the two-dimensional graphical language of string-nets, is an alternative description of the Turaev-Viro state sum model.
