Integral bases for TQFT modules and unimodular representations of mapping class groups

  • Patrick M. Gilmer

    Louisiana State University, Baton Rouge, USA
  • Gregor Masbaum

    Université Paris 7, Denis Diderot, Paris, France
  • Paul van Wamelen

    Louisiana State University, Baton Rouge, USA

Abstract

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, Gregor Masbaum, Paul van Wamelen, Integral bases for TQFT modules and unimodular representations of mapping class groups. Comment. Math. Helv. 79 (2004), no. 2, pp. 260–284

DOI 10.1007/S00014-004-0801-5