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Transactions of the American Mathematical Society

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Strong integrality of quantum invariants of 3-manifolds


Author: Thang T. Q. Lê
Journal: Trans. Amer. Math. Soc. 360 (2008), 2941-2963
MSC (2000): Primary 57M27; Secondary 57M25
DOI: https://doi.org/10.1090/S0002-9947-07-04359-0
Published electronically: December 11, 2007
MathSciNet review: 2379782
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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,\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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Additional Information

Thang T. Q. Lê
Affiliation: Department of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160
Email: letu@math.gatech.edu

DOI: https://doi.org/10.1090/S0002-9947-07-04359-0
Received by editor(s): March 2, 2006
Published electronically: December 11, 2007
Additional Notes: The author was supported in part by the National Science Foundation
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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