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

Patrick M. Gilmer·Gregor Masbaum·Paul van Wamelen
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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.

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Patrick M. Gilmer, Gregor Masbaum, Paul van Wamelen. 2002-07-11. Integral bases for TQFT modules and unimodular representations of mapping class groups. https://doi.org/10.1007/s00014-004-0801-5

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