Integral Lattices of the SU(2)-TQFT-Modules

Details Integral Lattices of the SU(2)-TQFT-Modules Integral Lattices of the SU(2)-TQFT-Modules

2007-12-05

arxiv.org/abs/0712.0669v2

Mathematics

Geometric Topology

10 pages This version has been just accepted at Kobe Journal of Mathematics

Scientific paper

We find bases for naturally defined lattices over certain rings of integers in the SU(2)-TQFT-theory modules of surfaces. We consider the TQFT where the Kauffman's A variable is a root of unity of order four times an odd prime. As an application, we show that the Frohman Kania-Bartoszynska ideal invariant for 3-manifolds with boundary using the SU(2)-TQFT-theory is equal to the product of the ideals using the 2^{'}-theory and the SO(3)-TQFT-theory under a certain change of coefficients.

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