Citation: Larsen, Michael, and Zhenghan Wang. "Density of the SO (3) TQFT representation of mapping class groups." Communications in mathematical physics 260.3 (2005): 641-658.
Web: https://arxiv.org/abs/math/0408161
Tags: Mathematical, TQFT, Fibonacci-anyons, Universal-scheme
In this paper, the authors compute images of the mapping class group representations associated to SO(3) Chern-Simmons TQFTs at prime level r>=5. They find that the imagine of the mapping class group representations on the torus is finite (in agreement with previous results of Kontsevich) and are equal to SL_2(F_r) or PSL_2(F_r) depending on whether r is congruent to 1 or -1 mod 4. On higher genus surfaces, the braid group action is shown to have dense image.
This paper really is just a hard-core calculation/computation using the theory of quantum groups (Lie theory), TQFTs, and modular tensor categories. It's a great paper to be aware of, and I am quite happy that Michael Larsen and Zhenghan Wang spent the time working out this example on this level of detail.