The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant
The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant
复制标题
有理同源 3 球体的微扰不变量可以从 LMO 不变量中恢复
DOI：
10.1112/jtopol/jts010
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
T. Ohtsuki
中科院分区：
文献类型：
--
作者：
T. Kuriya;T. T. Q. Le;T. Ohtsuki
证明了有理同调3-球面的微扰不变量可以从任意简单李代数的Le-Murakami-Ohtsuki（LMO）不变量中恢复出来，即LMO不变量是微扰不变量中的普适不变量.这种普适性在Le，Murakami and Ohtsuki ['On a universal perturbative invariant of 3‐ manifolds'，Topology 37（1998）539-574]中得到了证明。由于微扰不变量支配积分同调3-球面的量子不变量[K. Habiro，“On the quantum12 invariants of knots and integral homology spheres”，Invariants of knots and 3-manifold（京都2001），Geometry and Topology Monographs 4（Geometry and Topology Publications，Coventry，2002）161-181; K. Habiro，'A unified Witten-Reshetikhin-Turaev invariant for integral homology spheres'，171（2008）1-81; K. Habiro和T. T. Q. LMO不变量支配积分同调3-球的量子不变量。
We show that the perturbativeginvariant of rational homology 3‐spheres can be recovered from the Le‐Murakami‐Ohtsuki (LMO) invariant for any simple Lie algebrag, that is, the LMO invariant is universal among the perturbative invariants. This universality was conjectured in Le, Murakami and Ohtsuki [‘On a universal perturbative invariant of 3‐manifolds’,Topology37 (1998) 539–574]. Since the perturbative invariants dominate the quantum invariants of integral homology 3‐spheres [K. Habiro, ‘On the quantumsl2invariants of knots and integral homology spheres’,Invariants of knots and 3‐manifolds(Kyoto 2001), Geometry and Topology Monographs 4 (Geometry and Topology Publications, Coventry, 2002) 161–181; K. Habiro, ‘A unified Witten–Reshetikhin–Turaev invariant for integral homology spheres’, 171 (2008) 1–81; K. Habiro and T. T. Q. Le, in preparation] the LMO invariant dominates the quantum invariants of integral homology 3‐spheres.