Quantum Modularity for a Closed Hyperbolic 3-Manifold

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2025
• Main Author: Wheeler, Campbell
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2025
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212887
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Quantum Modularity for a Closed Hyperbolic 3-Manifold. Campbell Wheeler. SIGMA 21 (2025), 004, 74 pages

This paper proves quantum modularity of both functions from ℚ and -series associated to the closed manifold obtained by −1/2 surgery on the figure-eight knot, 4₁(−1, 2). In a sense, this is a companion to the work of Garoufalidis-Zagier, where similar statements were studied in detail for some simpl...