We construct integral bases for the -TQFT-modules of surfaces in genus one and two at roots of unity of prime order and show that the corresponding mapping class group representations preserve a unimodular Hermitian form over a ring of algebraic integers. For higher genus surfaces the Hermitian form sometimes must be non-unimodular. In one such case, genus three at a fifth root of unity, we still give an explicit basis.
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Patrick M. Gilmer, Paul van Wamelen, Gregor Masbaum, Integral bases for TQFT modules and unimodular representations of mapping class groups. Comment. Math. Helv. 79 (2004), no. 2, pp. 260–284DOI 10.1007/S00014-004-0801-5