Quantum invariants of random 3-manifolds

Abstract

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.

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

References in corpus (1)

• Geometry, Heegaard splittings and rank of the fundamental group of hyperbolic 3-manifolds

Cited by in corpus (3)

• Models of Random Knots
• All finite groups are involved in the Mapping Class Group
• Profinite completions of Burnside-type quotients of surface groups