Rigidity of $\mathbf{SU(2)}$ and $\mathbf{SO(3)}$ quantum representations of mapping class groups at prime levels

Pierre Godfard

paper

Rigidity of $SU (2)$ and $SO (3)$ quantum representations of mapping class groups at prime levels

arXiv:2511.19795

Abstract

We prove the rigidity of Witten-Reshetikhin-Turaev $SU (2)$ and $SO (3)$ quantum representations of mapping class groups at all prime levels for closed surfaces of genus at least $7$ . The proof relies on Ocneanu rigidity of modular categories and harmonic representatives in Hodge theory.

38 pages, 3 figures. Comments welcome!

Rigidity of SU(2) and SO(3) quantum representations of mapping class groups at prime levels

Abstract

Rigidity of $SU (2)$ and $SO (3)$ quantum representations of mapping class groups at prime levels