Strong integrality of quantum invariants of 3-manifolds

Lê, Thang

doi:10.1090/S0002-9947-07-04359-0

Strong integrality of quantum invariants of 3-manifolds
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by Thang T. Q. Lê PDF

Trans. Amer. Math. Soc. 360 (2008), 2941-2963 Request permission

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 $H_1(M,\mathbb {Z})$. An even stronger integrality, known as cyclotomic integrality, was established by Habiro for integral homology 3-spheres. Here we also generalize Habiro’s result to all rational homology 3-spheres.

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