论文标题
渐近乘法量子不变性
Asymptotically multiplicative quantum invariants
论文作者
论文摘要
欧拉的特征和体积是有限盖下歧管的两个最著名的乘法不变性。另一方面，3个manifolds的量子不变性不是乘法。 We show that a perturbative power series, introduced by Dimofte and the first author and shown to be a topological invariant of cusped hyperbolic 3-manifolds by Storzer--Wheeler and the first author, and conjectured to agree with the asymptotics of the Kashaev invariant to all orders in perturbation theory, is asymptotically multiplicative under cyclic covers.此外，其系数由扭曲的neumann-zagier数据构建的多项式确定。这给出了扰动量子不变的新的$ t $变形，与通过变形几何表示获得的$ x $变形不同。我们用几个双曲线结说明了结果。
The Euler characteristic and the volume are two best-known multiplicative invariants of manifolds under finite covers. On the other hand, quantum invariants of 3-manifolds are not multiplicative. We show that a perturbative power series, introduced by Dimofte and the first author and shown to be a topological invariant of cusped hyperbolic 3-manifolds by Storzer--Wheeler and the first author, and conjectured to agree with the asymptotics of the Kashaev invariant to all orders in perturbation theory, is asymptotically multiplicative under cyclic covers. Moreover, its coefficients are determined by polynomials constructed out of twisted Neumann--Zagier data. This gives a new $t$-deformation of the perturbative quantum invariants, different than the $x$-deformation obtained by deforming the geometric representation. We illustrate our results with several hyperbolic knots.
