On $p$-adic convergence of perturbative invariants of some rational homology spheres
On $p$-adic convergence of perturbative invariants of some rational homology spheres
复制标题
一些有理同调域的微扰不变量的$p$-adic收敛
DOI：
10.1215/s0012-7094-98-09115-3
复制
发表时间：
1996
影响因子：
2.5
通讯作者：
L. Rozansky
中科院分区：
文献类型：
--
作者：
L. Rozansky
R.~ Lawrence证明了对于有理同调球面，Ohtsuki不变量的级数p-逼近地收敛于SO（3）Witten-Reshetikhin-Turaev不变量。我们证明了这个猜想的塞弗特有理同调球。我们还导出了通过对S^3中的一个纽结进行外科手术而构造的流形。我们的推导是基于一个猜想的有色琼斯多项式，我们已经制定了我们以前的文件。我们还提出了一些简单的流形的p-adic收敛的数值例子。
R.~Lawrence has conjectured that for rational homology spheres, the series of Ohtsuki's invariants converges p-adicly to the SO(3) Witten-Reshetikhin-Turaev invariant. We prove this conjecture for Seifert rational homology spheres. We also derive it for manifolds constructed by a surgery on a knot in S^3. Our derivation is based on a conjecture about the colored Jones polynomial that we have formulated in our previous paper. We also present numerical examples of p-adic convergence for some simple manifolds.