Hecke-type formulas for families of unified Witten-Reshetikhin-Turaev invariants

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2017-01-01 DOI:10.4310/CNTP.2017.V11.N2.A1

K. Hikami, Jeremy Lovejoy

引用次数: 6

Abstract

Every closed orientable 3-manifold can be constructed by surgery on a link in S. In the case of surgery along a torus knot, one obtains a Seifert fibered manifold. In this paper we consider three families of such manifolds and study their unified WittenReshetikhin-Turaev (WRT) invariants. Thanks to recent computation of the coefficients in the cyclotomic expansion of the colored Jones polynomial for (2, 2t+ 1)-torus knots, these WRT invariants can be neatly expressed as q-hypergeometric series which converge inside the unit disk. Using the Rosso-Jones formula and some rather non-standard techniques for Bailey pairs, we find Hecke-type formulas for these invariants. We also comment on their mock and quantum modularity.

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统一Witten-Reshetikhin-Turaev不变量族的hecke型公式

每一个闭合的可定向3流形都可以通过在s中的连杆上进行手术来构造。在沿环面结进行手术的情况下，可以得到一个Seifert纤维流形。本文考虑了这类流形的三个族，并研究了它们的统一WittenReshetikhin-Turaev (WRT)不变量。由于最近对(2,2t + 1)-环面结的彩色琼斯多项式的分环展开中的系数的计算，这些WRT不变量可以整齐地表示为收敛于单位圆盘内的q超几何级数。使用Rosso-Jones公式和一些非标准的贝利对技术，我们找到了这些不变量的赫克式公式。我们还评论了它们的模拟和量子模块化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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