论文标题
Witten-Reshetikhin-turaev不变和钢管同源球的同源块
Witten-Reshetikhin-Turaev invariants and homological blocks for plumbed homology spheres
论文作者
论文摘要
在本文中，我们证明了Gukov-Pei-Putrov-Vafa的猜想是一类宽类的3型物体。他们的猜想指出，Witten-Reshetikhin-Turaev（WRT）不变性是同源块的径向限制，这是它们为$ q $ series引入的$ q $ series，用于底管的3个manifolds，具有负面的确定链接矩阵。我们证明中最困难的点是证明加权高斯总和消失了，这些加权总和在同源块的渐近扩展中以负程度的系数出现。为了处理它，我们开发了一种针对渐近扩展的新技术，这使我们能够分别比较有理功能的渐近扩展和与WRT不变性和同源块有关的错误theta函数。在我们的技术中，我们消失的结果取决于这种理性功能的全体形状。
In this paper, we prove a conjecture by Gukov-Pei-Putrov-Vafa for a wide class of plumbed 3-manifolds. Their conjecture states that Witten-Reshetikhin-Turaev (WRT) invariants are radial limits of homological blocks, which are $ q $-series introduced by them for plumbed 3-manifolds with negative definite linking matrices. The most difficult point in our proof is to prove the vanishing of weighted Gauss sums that appear in coefficients of negative degree in asymptotic expansions of homological blocks. To deal with it, we develop a new technique for asymptotic expansions, which enables us to compare asymptotic expansions of rational functions and false theta functions related to WRT invariants and homological blocks, respectively. In our technique, our vanishing results follow from holomorphy of such rational functions.
