On the TQFT representations of the mapping class groups

Louis Funar

Vol. 188 (1999), No. 2, 251–274

DOI: 10.2140/pjm.1999.188.251

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.

Milestones

Received: 10 June 1997

Revised: 15 December 1997

Published: 1 March 1999