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Strong integrality of quantum invariants of 3-manifolds

Author(s): Thang T. Q. Lê
Journal: Trans. Amer. Math. Soc. 360 (2008), 2941-2963.
MSC (2000): Primary 57M27; Secondary 57M25
Posted: December 11, 2007
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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: 10.1090/S0002-9947-07-04359-0
PII: S 0002-9947(07)04359-0
Received by editor(s): March 2, 2006
Posted: December 11, 2007
Additional Notes: The author was supported in part by the National Science Foundation
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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