Strong integrality of quantum invariants of 3-manifolds
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- by Thang T. Q. Lê PDF
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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.References
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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
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2379782