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arXiv 0712.0669math.GT
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SU(2)-TQFT-模的整格

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

Khaled Qazaqzeh

摘要:

我们在SU(2)-TQFT-理论曲面模中找到了某些整数环上自然定义格的基。我们考虑的TQFT的考夫曼的A变量是一个单位根的顺序四次奇素数。作为应用,我们证明了在一定的系数变化下,利用SU(2)-TQFT理论得到的3-流形的Frohman Kania-Bartoszynska理想不变量等于利用2^^'}-理论和SO(3)-TQFT理论得到的理想的乘积.

英文摘要:

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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