Quantum modular forms and plumbing graphs of 3-manifolds

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:170

Article

Bringmann, Kathrin¹  Mahlburg, Karl²  Milas, Antun³ 

[1] Univ Cologne, Math Inst, Weyertal 86-90, D-50931 Cologne, Germany

[2] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

[3] SUNY Albany, Dept Math & Stat, Albany, NY 12222 USA

关键词: Quantum invariants;    Plumbing graphs;    Quantum modular forms;    Cartan matrices;   

DOI  :  10.1016/j.jcta.2019.105145

来源: Elsevier

【 摘 要 】

In this paper, we study quantum modular forms in connection to quantum invariants of plumbed 3-manifolds introduced recently by Gukov, Pei, Putrov, and Vafa. We explicitly compute these invariants for any 3-leg star plumbing graphs whose associated matrix is unimodular and positive definite. For these graphs we confirm a quantum modularity conjecture of Gukov. We also analyze the invariants for general n-leg star graphs with unimodular plumbing matrices, and prove that they can be expressed as linear combinations of quantum modular forms. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free