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Strong Integrality of Quantum Invariants of 3-manifolds

Thang T. Q. Le
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Abstract

We prove that the quantum SO(3)-invariant of an arbitrary 3-manifold $M$ is always an algebraic integer, if the order of the quantum parameter is co-prime with the order of the torsion part of $H_1(M,\BZ)$. An even stronger integrality, known as cyclotomic integrality, was established by Habiro for integral homology 3-spheres. Here we generalize Habiro's result to all rational homology 3-spheres.

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Thang T. Q. Le. 2006-01-26. Strong Integrality of Quantum Invariants of 3-manifolds. https://arxiv.org/abs/math/0512433

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