2026/08/05 by Liang Chang, Siu-Hung Ng, Yilong Wang
Mathematics · #math.QA #math.GT #math.RT
arxiv created 2026/08/05 · arxiv updated 2026/08/06
In this paper, we study modular fusion categories whose mapping class group representations are trivial on the Torelli groups, with particular emphasis on the congruence properties of the resulting representations of Sp(2g,ℤ). We prove that, for any g ≥ 3, the Torelli group is contained in the kernel of the genus-g mapping class group representation ρg associated with a modular fusion category C if and only if C is pointed. This refines the corresponding result in \citeMW25. We also characterize the modular fusion categories for which the genus-2 Torelli group is contained in ker ρ2; in particular, categories with isotropic adjoint subcategories belong to this class. Finally, we give a complete classification of modular fusion categories with isotropic adjoint subcategories.