Free subgroups within the images of quantum representations

Abstract

We prove that, except for a few explicit roots of unity, the quantum image of any Johnson subgroup of the mapping class group contains an explicit free non-abelian subgroup.

revised version 14p., 4 figures. We removed the sections containing applications of the largeness results presented here to finite index subgroups of mapping class groups, as the proofs in the former version have a gap. arXiv admin note: substantial text overlap with arXiv:0907.0568