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On the TQFT representations of the mapping class groups

1999
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Pacific Journal of Mathematics
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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. 2. Preliminaries. Hecke algebras and Temperley-Lieb algebras. We will outline briefly, for the sake of completeness, some

doi:10.2140/pjm.1999.188.251
fatcat:yhlfdsju7jdctaivfzycyffay4