Integral bases for TQFT modules and unimodular representations of mapping class groups
Quantum Algebra
2015-12-22 v1 Geometric Topology
Abstract
We construct integral bases for the 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 3 and p=5, we still give an explicit basis.
Cite
@article{arxiv.math/0207093,
title = {Integral bases for TQFT modules and unimodular representations of mapping class groups},
author = {Patrick M. Gilmer and Gregor Masbaum and Paul van Wamelen},
journal= {arXiv preprint arXiv:math/0207093},
year = {2015}
}