Ẑ and Splice Diagrams

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2025
• Main Authors: Gukov, Sergei, Katzarkov, Ludmil, Svoboda, Josef
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2025
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/214173
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Ẑ and Splice Diagrams. Sergei Gukov, Ludmil Katzarkov and Josef Svoboda. SIGMA 21 (2025), 073, 30 pages

We study quantum q-series invariants of 3-manifolds Ẑσ of Gukov-Pei-Putrov-Vafa, using techniques from the theory of normal surface singularities such as splice diagrams. We show that the (suitably normalized) sum of all Ẑσ depends only on the splice diagram, and in particular, it agrees for manifol...