Asymptotic properties of the quantum representations of the modular group

Details Asymptotic properties of the quantum representations of the modular group Asymptotic properties of the quantum representations of the modular group

2010-05-19

arxiv.org/abs/1005.3447v1

Mathematics

Geometric Topology

38 pages

Scientific paper

We study the asymptotic behaviour of the quantum representations of the modular group in the large level limit. We prove that each element of the modular group acts as a Fourier integral operator. This provides a link between the classical and quantum Chern-Simons theories for the torus. From this result we deduce the known asymptotic expansion of the Witten-Reshetikhin-Turaev invariants of the torus bundles with hyperbolic monodromy.

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