On the TQFT representations of the mapping class groups

Abstract

We prove that the image of the mapping class group by the representations arising in the SU (2)-TQFT is infinite, provided that the genus g 2 and the level of the theory r = 2, 3, 4, 6 (and r = 10 for g = 2). In particular it follows that the quotient groups M g /N (t r ) by the normalizer of the r-th power of a Dehn twist t are infinite if g 3 and r = 2, 3, 4, 6, 8, 12.