Quantum invariants of random 3–manifolds

Dunfield, Nathan M; Wong, Helen

doi:10.2140/agt.2011.11.2191

¹Department of Mathematics, University of Illinois, Urbana IL 61801, USA
²Department of Mathematics, Carleton College, 1 North College Street, Northfield MN 55057, USA

Algebraic and Geometric Topology, Tome 11 (2011) no. 4, pp. 2191-2205

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Résumé

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 10−7 except when g ≤ 3. We also examine random surface bundles over the circle and find the same distribution for quantum invariants there.

DOI : 10.2140/agt.2011.11.2191

Classification : 57M27, 57N10
Keywords: quantum invariants, random 3–manifolds, Heegaard genus

Affiliations des auteurs :

Dunfield, Nathan M ¹ ; Wong, Helen ²

¹ Department of Mathematics, University of Illinois, Urbana IL 61801, USA
² Department of Mathematics, Carleton College, 1 North College Street, Northfield MN 55057, USA

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     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2011.11.2191/}
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Dunfield, Nathan M; Wong, Helen. Quantum invariants of random 3–manifolds. Algebraic and Geometric Topology, Tome 11 (2011) no. 4, pp. 2191-2205. doi: 10.2140/agt.2011.11.2191

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