论文标题
时期，Meromormorphic 3D索引和Turaev-Viro不变
Periods, the meromorphic 3D-index and the Turaev--Viro invariant
论文作者
论文摘要
Dimofte-Gaiotto-Gukov的3D索引是一个有趣的$ Q $ series集合，其整数系数由一对整数参数，并与带有圆环边界的3个manifold相关联。在本说明中，我们解释了3D索引的渐近扩展的结构时，当$ q = e^{2πiτ} $和$τ$趋于零（对所有订单而言，包括所有订单，包括指数的小术语），并发现两个现象：（a）$τ$在$τ$接近正面的现实轴心上的范围内趋于零，则趋于3d-index。 orders with the asymptotics of the Turaev-Viro invariant of a knot, in particular explaining the Volume Conjecture of Chen-Yang from first principles, (b) when $τ\to 0$ on the positive imaginary axis, the vertical asymptotics of the 3D-index involves periods of a plane curve (the $A$-polynomial), as opposed to algebraic numbers, explaining some predictions Hodgson-Kricker-siejakowski的作品，并在$ a $ polynomial的$ polynomial和Euler beta功能的积分之间提出了猜想的身份。
The 3D-index of Dimofte-Gaiotto-Gukov is an interesting collection of $q$-series with integer coefficients parametrised by a pair of integers and associated to a 3-manifold with torus boundary. In this note, we explain the structure of the asymptotic expansions of the 3D-index when $q=e^{2πiτ}$ and $τ$ tends to zero (to all orders and with exponentially small terms included), and discover two phenomena: (a) when $τ$ tends to zero on a ray near the positive real axis, the horizontal asymptotics of the meromorphic 3D-index match to all orders with the asymptotics of the Turaev-Viro invariant of a knot, in particular explaining the Volume Conjecture of Chen-Yang from first principles, (b) when $τ\to 0$ on the positive imaginary axis, the vertical asymptotics of the 3D-index involves periods of a plane curve (the $A$-polynomial), as opposed to algebraic numbers, explaining some predictions of Hodgson-Kricker-Siejakowski and leading to conjectural identities between periods of the $A$-polynomial of a knot and integrals of the Euler beta-function.
