Generalized property F for weakly group-theoretical modular fusion categories
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.
Related
- The Grothendieck Ring of Strictly Weakly Integral Fusion Categories of Rank 6
- An Ito-Michler type theorem and the prime class graph of weakly integral braided fusion categories
- Commutative exact algebras and modular tensor categories
- Pre-modular fusion categories of global dimension 2p
- Property F and weak integrality of braided fusion categories
BibTeX
@misc{li2026generalized,
title = {{Generalized property F for weakly group-theoretical modular fusion categories}},
author = {Enyu Li and Yuze Ruan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05177},
eprint = {2610.05177},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05177},
}
RIS
TY - UNPB
TI - Generalized property F for weakly group-theoretical modular fusion categories
AU - Enyu Li
AU - Yuze Ruan
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05177
UR - https://arxiv.org/abs/2610.05177
AB - 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.
ER -