Algebraic & Geometric Topology

Quantum invariants of random 3–manifolds

Nathan M Dunfield and Helen Wong

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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 107 except when g3. We also examine random surface bundles over the circle and find the same distribution for quantum invariants there.

Article information

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

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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]

quantum invariants random 3–manifolds Heegaard genus


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.

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