#### Volume 11, issue 4 (2011)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
Quantum invariants of random 3–manifolds

### Nathan M Dunfield and Helen Wong

Algebraic & Geometric Topology 11 (2011) 2191–2205
##### Abstract

We consider the $SO\left(3\right)$ 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 $1{0}^{-7}$ except when $g\le 3$. 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
Primary: 57M27
Secondary: 57N10