弱群论模融合范畴的广义性质F
Generalized property F for weakly group-theoretical modular fusion categories
- Qiuzhen College, Tsinghua University（清华大学邱氏学院）
- Yau Mathematical Sciences Center and Department of Mathematics, Tsinghua University（清华大学丘成桐数学科学中心及数学系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明弱群论模融合范畴具有广义性质F，即其Reshetikhin-Turaev映射类群表示对紧致定向曲面具有有限射影像，推广了早期结果并扩展至完整映射类群。
AI中文摘要：
我们证明了每个弱群论模融合范畴，配备其典范正球面结构，具有广义性质F：相关的Reshetikhin-Turaev映射类群表示，对于所有带有标记框架点的紧致定向曲面，具有有限射影像。这推广了早期关于与弱群论辫子融合范畴相关的辫群表示的有限像结果，以及与群论模融合范畴和Ising范畴相关的映射类群表示的有限像结果。在弱群论设置中，它还将闭曲面对称映射类群的已知有限性结果扩展到完整映射类群。
英文摘要：
We prove that every weakly group-theoretical modular fusion category, equipped with its canonical positive spherical structure, has generalized property F: the associated Reshetikhin-Turaev mapping class group representations have finite projective image for all compact oriented surfaces with labeled framed points. This generalizes earlier finite-image results for braid group representations associated with weakly group-theoretical braided fusion categories and for mapping class group representations associated with group-theoretical modular fusion categories and Ising categories. In the weakly group-theoretical setting, it also extends the known finiteness result for symmetric mapping class groups of closed surfaces to the full mapping class groups.
