Integral bases for TQFT modules and unimodular representations of mapping class groups
Patrick M. GilmerLouisiana State University, Baton Rouge, USA
Paul van WamelenLouisiana State University, Baton Rouge, USA
Gregor MasbaumUniversité Paris 7, Denis Diderot, Paris, France
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.
Cite this article
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