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

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

2002-07-11

arxiv.org/abs/math/0207093v1

Mathematics

Quantum Algebra

Scientific paper

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.

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