JournalscmhVol. 79, No. 2pp. 260–284

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

  • Patrick M. Gilmer

    Louisiana State University, Baton Rouge, USA
  • Paul van Wamelen

    Louisiana State University, Baton Rouge, USA
  • Gregor Masbaum

    Université Paris 7, Denis Diderot, Paris, France
Integral bases for TQFT modules and unimodular representations of mapping class groups cover
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Abstract

We construct integral bases for the SO(3)SO(3)-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. 260–284

DOI 10.1007/S00014-004-0801-5