Abstract
We consider the Witten–Reshetikhin–Turaev quantum invariants of random 3–manifolds. When the level is prime, we show that the asymptotic distribution of the absolute value of these invariants is given by a Rayleigh distribution which is 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 is positive but very small, less than except when . We also examine random surface bundles over the circle and find the same distribution for quantum invariants there.
Citation
Nathan M Dunfield. Helen Wong. "Quantum invariants of random 3–manifolds." Algebr. Geom. Topol. 11 (4) 2191 - 2205, 2011. https://doi.org/10.2140/agt.2011.11.2191
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