AI 中文总结
本文构造三维定向配边双范畴的$\boldsymbol{\text{Z}}$中心扩张半符号配边双范畴$\boldsymbol{\text{Bord}}_{1,2,3}^{\text{sig}/2}$，遵循Bartlett等人的方法构造其展示，证明其线性表示由模张量范畴分类。
AI 中文摘要
我们将半符号配边双范畴$\boldsymbol{\text{Bord}}_{1,2,3}^{\text{sig}/2}$构造为三维定向配边双范畴的$\boldsymbol{\text{Z}}$中心扩张，它是符号配边双范畴的指数为2的子扩张。遵循Bartlett--Douglas--Schommer-Pries--Vicary的方法，我们构造该双范畴的展示，从而证明其线性表示恰好由模张量范畴分类。
英文摘要
We construct the half-signature bordism bicategory $\mathbf{Bord}_{1,2,3}^\mathrm{sig/2}$ as a central extension of the 3-dimensional oriented bordism bicategory by $\mathbb{Z}$. This is an index $2$ subextension of the signature bordism bicategory. Following methods of Bartlett--Douglas--Schommer-Pries--Vicary, we construct a presentation of this bicategory and hence show that its linear representations are classified exactly by modular tensor categories.
Comments52 pages, many diagrams, comments welcome
