Algebraic & Geometric Topology 11 (2011) 2191–2205

DOI: 10.2140/agt.2011.11.2191

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 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 g is positive but very small, less than 10⁻⁷ except when g ≤ 3. We also examine random surface bundles over the circle and find the same distribution for quantum invariants there.

Keywords

quantum invariants, random 3–manifolds, Heegaard genus

Mathematical Subject Classification

Primary: 57M27

Secondary: 57N10

References

Publication

Received: 10 September 2010
Accepted: 21 June 2011
Published: 29 July 2011

Authors