English

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

Geometric Topology 2025-11-26 v1 Algebraic Geometry Quantum Algebra

Abstract

We prove the rigidity of Witten-Reshetikhin-Turaev SU(2)\mathrm{SU}(2) and SO(3)\mathrm{SO}(3) quantum representations of mapping class groups at all prime levels for closed surfaces of genus at least 77. The proof relies on Ocneanu rigidity of modular categories and harmonic representatives in Hodge theory.

Keywords

Cite

@article{arxiv.2511.19795,
  title  = {Rigidity of $\mathbf{SU(2)}$ and $\mathbf{SO(3)}$ quantum representations of mapping class groups at prime levels},
  author = {Pierre Godfard},
  journal= {arXiv preprint arXiv:2511.19795},
  year   = {2025}
}

Comments

38 pages, 3 figures. Comments welcome!