Norm estimates and asymptotic faithfulness of the quantum $SU(n)$ representations of the mapping class groups

Abstract

We give a direct proof for the asymptotic faithfulness of the quantum $SU(n)$ representations of the mapping class groups using peak sections in Kodaira embedding. We give also estimates on the norm of the parallell transport of the projective connection on the Verlinde bundle. The faithfulness has been proved earlier in [1] using Toeplitz operators of compact Kähler manifolds and in [10] using skein theory.

Geometriae Dedicata (online), 10 pages, minor changes

References in corpus (1)

• Quantum SU(2) faithfully detects mapping class groups modulo center