Quantum invariants of 3-manifolds: integrality, splitting, and perturbative expansion

Details Quantum invariants of 3-manifolds: integrality, splitting, and perturbative expansion Quantum invariants of 3-manifolds: integrality, splitting, and perturbative expansion

2000-04-15

arxiv.org/abs/math/0004099v1

Mathematics

Quantum Algebra

26 pages

Scientific paper

We consider quantum invariants of 3-manifolds associated with arbitrary simple Lie algebras. Using the symmetry principle we show how to decompose the quantum invariant as the product of two invariants, one of them is the invariant corresponding to the projective group. We then show that the projective quantum invariant is always an algebraic integer, if the quantum parameter is a prime root of unity. We also show that the projective quantum invariant of rational homology 3-spheres has a perturbative expansion a la Ohtsuki. The presentation of the theory of quantum 3-manifold is self-contained.

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