Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 11, Number 4 (2011), 2191-2205.
Quantum invariants of random 3–manifolds
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.
Algebr. Geom. Topol., Volume 11, Number 4 (2011), 2191-2205.
Received: 10 September 2010
Accepted: 21 June 2011
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Dunfield, Nathan M; Wong, Helen. Quantum invariants of random 3–manifolds. Algebr. Geom. Topol. 11 (2011), no. 4, 2191--2205. doi:10.2140/agt.2011.11.2191. https://projecteuclid.org/euclid.agt/1513715266