Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Li, Enyu, Ruan, Yuze
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220670495