Integral bases for certain TQFT-modules of the torus

• Autores: Khaled Qazaqzeh
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 143, Nº 3, 2007, págs. 669-684
• Idioma: inglés
• DOI: 10.1017/s030500410700059x
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• Resumen

  • We find two bases for the lattices of the SU(2)-TQFT-theory modules of the torus over given rings of integers. One basis is a variation on the bases defined in [GMW] for the lattices of the SO(3)-TQFT-theory modules of the torus. Moreover, we discuss the quantization functors (Vp, Zp) for p = 1, and p = 2. Then we give concrete bases for the lattices of the modules in the 2-theory. We use the above results to discuss the ideal invariant defined in [FK]. The ideal can be computed for all the 3-manifolds using the 2-theory, and for all 3-manifolds with torus boundary using the SU(2)-TQFT-theory. In fact, we show that this ideal using the SU(2)-TQFT-theory is contained in the product of the ideals using the 2-theory and the SO(3)-TQFT-theory under a certain change of coefficients, and with equality in the case of torus boundary.