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 -invariant of an arbitrary 3-manifold is always an algebraic integer if the order of the quantum parameter is co-prime with the order of the torsion part of . 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.