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24 pages, PACIFIC JOURNAL OF MATHEMATICS, Vol. 188, No. 2, 1999

Abstract:

The author proves 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 or = 2, and the level of the theory r is not equal to 6= 2;3;4;6 (and r is different form 10 for g = 2)". Backgorund: "Witten constructed a TQFT in dimension 3 using path integrals and afterwards several rigorous constructions arose, like those using the quantum group approach, the Temperley-Lieb algebra, the theory based on the Kauffman bracket, or the theory obtained from the mapping class group representations and the conformal field theory." Any TQFT gives rise to a tower of representations of the mapping class groups M_g in all genera g, and such a tower determines in fact the theory (up to the choice of the vacuum vector, as shown previously). (Free on line download at: http://nyjm.albany.edu:8000/PacJ/p/1999/188-2-5.pdf )

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