Strong Integrality of Quantum Invariants of 3-manifolds

Thang T. Q. Le

Strong Integrality of Quantum Invariants of 3-manifolds

Geometric Topology 2007-05-23 v2 Quantum Algebra

Authors: Thang T. Q. Le

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

Keywords

quantum invariants 3-manifolds algebraic integer cyclotomic integrality so(3)-invariant rational homology sphere

Cite

@article{arxiv.math/0512433,
  title  = {Strong Integrality of Quantum Invariants of 3-manifolds},
  author = {Thang T. Q. Le},
  journal= {arXiv preprint arXiv:math/0512433},
  year   = {2007}
}

Comments

19 pages. Minor typos corrected

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