Algebraic & Geometric Topology

Quantum invariants of random 3–manifolds

Nathan M Dunfield and Helen Wong

Full-text: Open access

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.

Article information

Source
Algebr. Geom. Topol., Volume 11, Number 4 (2011), 2191-2205.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715266

Digital Object Identifier
doi:10.2140/agt.2011.11.2191

Mathematical Reviews number (MathSciNet)
MR2826936

Zentralblatt MATH identifier
1236.57017

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57N10: Topology of general 3-manifolds [See also 57Mxx]

Keywords
quantum invariants random 3–manifolds Heegaard genus

Citation

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


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