Quantum invariants of 3-manifolds: Integrality, splitting, and perturbative expansion
Quantum invariants of 3-manifolds: Integrality, splitting, and perturbative expansion
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三流形的量子不变量：积分、分裂和微扰展开
DOI：
10.1016/s0166-8641(02)00056-1
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发表时间：
2000
影响因子：
0.6
通讯作者：
Thang T. Q. Lê
中科院分区：
文献类型：
--
作者：
Thang T. Q. Lê
本文研究了与任意单李代数相关的三维流形的量子不变量。利用对称性原理，我们证明了如何将量子不变量分解为两个不变量的乘积，其中一个是对应于投射群的不变量。然后，我们表明，投影量子不变量总是一个代数整数，如果量子参数是一个单位的素根。我们还证明了有理同调3-球面的射影量子不变量具有Ohtsuki微扰展开。量子三维流形不变量理论的表述是完备的。
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 invariants is self-contained.