Volume 11, issue 4 (2011)

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Quantum invariants of random 3–manifolds

Nathan M Dunfield and Helen Wong

Algebraic & Geometric Topology 11 (2011) 2191–2205
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 g 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
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57N10
References
Publication
Received: 10 September 2010
Accepted: 21 June 2011
Published: 29 July 2011
Authors
Nathan M Dunfield
Department of Mathematics
University of Illinois
Urbana IL 61801
USA
http://dunfield.info/
Helen Wong
Department of Mathematics
Carleton College
1 North College Street
Northfield MN 55057
USA
http://people.carleton.edu/~hwong/