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2011 Quantum invariants of random 3–manifolds
Nathan M Dunfield, Helen Wong
Algebr. Geom. Topol. 11(4): 2191-2205 (2011). 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 107 except when g3. We also examine random surface bundles over the circle and find the same distribution for quantum invariants there.

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Nathan M Dunfield. Helen Wong. "Quantum invariants of random 3–manifolds." Algebr. Geom. Topol. 11 (4) 2191 - 2205, 2011. https://doi.org/10.2140/agt.2011.11.2191

Information

Received: 10 September 2010; Accepted: 21 June 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1236.57017
MathSciNet: MR2826936
Digital Object Identifier: 10.2140/agt.2011.11.2191

Subjects:
Primary: 57M27
Secondary: 57N10

Rights: Copyright © 2011 Mathematical Sciences Publishers

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