Quantum invariants of random 3-manifolds

Details Quantum invariants of random 3-manifolds Quantum invariants of random 3-manifolds

2010-09-08

arxiv.org/abs/1009.1653v2

Mathematics

Geometric Topology

12 pages; V2 minor changes, to appear in Alg. Geom. Top

Scientific paper

We consider the SO(3) Witten-Reshetikhin-Turaev quantum invariants of random 3-manifolds. When the level r is prime, we show that the asymptotic distribution of the absolute value of these invariants is given by the standard Rayleigh distribution and independent of the choice of level. Hence the probability that the quantum invariant certifies the Heegaard genus of a random 3-manifold of a fixed Heegaard genus g is positive but very small, less than 10^-7 except when g < 4. We also examine random surface bundles over the circle and find the same distribution for quantum invariants there.

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