Year: 2026
Type: article
Abstract: We prove that braid group representations associated to braided fusion categories and mapping class group representations associated to modular fusion categories are always semisimple. The proof relies on the theory of extensions in non-Abelian Hodge theory and on Ocneanu rigidity. By combining this with previous results on the existence of variations of Hodge structure, we further show that such a braid group or mapping class group representation preserves a non-degenerate Hermitian form and can be defined over some CM number field.
Author: Pierre Godfard
Institution: University of North Carolina at Chapel Hill
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416101655